Give an example of two square matrices of order 2x2 each so that

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Short Answer Type

91.

If $straight A equals space open square brackets table row 0 0 1 row 0 1 0 row 1 0 0 end table close square brackets comma space$ verify that $straight A squared space equals space 1.$

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Long Answer Type

92.

If $straight A equals open square brackets table row 1 cell space space 2 end cell row 3 cell space space 4 end cell row 5 cell space space 6 end cell end table close square brackets space and space straight B equals open square brackets table row 4 cell space 5 end cell cell space space 6 end cell row 7 cell space 8 end cell cell space space 9 end cell end table close square brackets$ then find AB and BA. Is AB= BA ? What conclusion do you draw?

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93.

$If space straight A equals open square brackets table row 2 cell negative 1 end cell 3 row cell negative 3 end cell 2 0 row 5 1 cell negative 1 end cell end table close square brackets comma straight B equals space open square brackets table row cell negative 3 end cell 2 cell negative 1 end cell row 0 5 2 row 1 cell negative 2 end cell cell negative 1 end cell end table close square brackets space then find space AB space and space BA. space Is space AB equals BA ? space What space conclusion space do space you space draw$

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Short Answer Type

94.

show that $open square brackets table row 5 cell space minus 1 end cell row 6 cell space space space space 7 end cell end table close square brackets open square brackets table row 2 cell space 1 end cell row 3 cell space 4 end cell end table close square brackets not equal to open square brackets table row 2 cell space 1 end cell row 3 cell space 4 end cell end table close square brackets open square brackets table row cell 5 space space end cell cell negative 1 end cell row 6 cell space space space 7 end cell end table close square brackets$

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95.

show that $open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets not equal to open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets$

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96.

If space straight A equals open square brackets table row 1 cell negative 1 end cell 1 row 0 2 1 end table close square brackets comma space straight B space open square brackets table row 1 cell negative 1 end cell 0 row 0 1 cell negative 1 end cell row 1 1 1 end table close square brackets space comma straight C space open square brackets table row 1 0 row 0 1 row 1 1 end table close square brackets space verify space that space straight A space left parenthesis BC right parenthesis equals left parenthesis AB right parenthesis space straight C.

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Long Answer Type

97.

if space straight A equals open square brackets table row 1 1 1 row 2 0 cell negative 3 end cell row 3 cell negative 1 end cell 2 end table close square brackets comma straight B equals open square brackets table row 1 3 row 0 2 row cell negative 1 end cell 4 end table close square brackets comma space and space straight C equals open square brackets table row 1 2 3 cell negative 4 end cell row 2 0 cell negative 2 end cell 1 end table close square brackets

Find A(BC), (AB)C and show that (AB(BC).)C=A(BC)

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Short Answer Type

98.

If space straight A equals open square brackets table row 0 cell space space 6 end cell cell space 7 end cell row cell negative 6 end cell cell space space space 0 end cell cell space 8 end cell row 7 cell negative 8 end cell cell space 0 end cell end table close square brackets space comma space straight B equals open square brackets table row 0 cell space space 1 end cell cell space space 1 end cell row 1 cell space space 0 end cell cell space 2 end cell row 1 cell space space 2 end cell cell space 0 end cell end table close square brackets space comma space straight C equals open square brackets table row cell space space space space 2 end cell row cell negative 2 end cell row cell space space space 3 end cell end table close square brackets

Calculate AC,BC and (A+B) C. Also, verify that (A+B) C-AC+BC.

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99.

if space straight A space equals open square brackets table row 1 cell negative 1 end cell row 2 3 end table close square brackets comma space straight B space open square brackets table row 2 cell space 1 end cell row 1 cell space 0 end cell end table close square brackets space comma space verify space that space left parenthesis straight A plus straight B right parenthesis squared space not equal to space straight A squared space plus 2 AB plus straight B squared

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100.
Give an example of two square matrices of order 2x2 each so that $left parenthesis straight A plus straight B right parenthesis squared equals straight A squared plus 2 AB plus straight B squared$

Let space straight A equals open square brackets table row 1 cell space space 2 end cell row cell negative 2 end cell cell space space 1 end cell end table close square brackets space comma space straight B space equals open square brackets table row 3 cell space minus 4 end cell row 4 cell space space space space space 3 end cell end table close square brackets therefore space straight A plus straight B space equals space open square brackets table row 4 cell space space minus 2 end cell row 2 cell space space space space space space space 4 end cell end table close square brackets space open square brackets table row 4 cell space space minus 2 end cell row 2 cell space space space space space space space space 4 end cell end table close square brackets equals space open square brackets table row cell 16 minus 4 space end cell cell negative 8 minus 8 end cell row cell 8 plus 8 end cell cell space space minus 4 plus 16 end cell end table close square brackets equals open square brackets table row cell 12 space end cell cell negative 16 end cell row 16 cell space space 12 end cell end table close square brackets therefore left parenthesis straight A plus straight B right parenthesis squared equals space open square brackets table row 12 cell space space minus 16 end cell row 16 cell space space space space space space 12 end cell end table close square brackets space space space space space space space space space space space space space space space space space space straight A squared space equals space open square brackets table row 1 cell space space 2 end cell row cell negative 2 end cell cell space space 1 end cell end table close square brackets space open square brackets table row 1 cell space space space 2 end cell row cell negative 2 end cell cell space space 1 end cell end table close square brackets space equals open square brackets table row cell 1 minus 4 end cell cell space space space 2 plus 2 end cell row cell negative 2 minus 2 end cell cell space minus 4 plus 1 end cell end table close square brackets equals open square brackets table row cell negative 3 end cell cell space space 4 end cell row cell negative 4 space end cell cell negative 3 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space straight B squared equals open square brackets table row 3 cell space minus 4 end cell row 4 cell space space space space space space 3 end cell end table close square brackets space space space open square brackets table row 3 cell negative 4 end cell row 4 3 end table close square brackets equals space open square brackets table row cell 9 minus 16 end cell cell space minus 12 minus 1 end cell row cell 12 plus 12 end cell cell space minus 16 plus 9 end cell end table close square brackets equals open square brackets table row cell negative 7 end cell cell space space 24 end cell row 24 cell negative 7 end cell end table close square brackets space space space space space space space space space space space space space space AB space space equals space open square brackets table row 1 cell space space 2 end cell row cell negative 2 end cell 1 end table close square brackets space open square brackets table row 3 cell negative 4 end cell row cell negative 4 end cell 3 end table close square brackets equals open square brackets table row cell 3 plus 8 end cell cell negative 4 plus 6 end cell row cell negative 6 plus 8 end cell cell 8 plus 3 end cell end table close square brackets equals open square brackets table row 11 cell space space space space 2 end cell row cell negative 2 end cell cell space 11 end cell end table close square brackets therefore space space space 2 AB space equals open square brackets table row 22 cell space 4 end cell row cell negative 4 end cell cell space space 22 end cell end table close square brackets therefore space space straight A squared plus straight B squared space equals space open square brackets table row 12 cell negative 16 end cell row 16 12 end table close square brackets space space straight A squared space equals space open square brackets table row 1 cell space 2 end cell row cell negative 2 end cell cell space 1 end cell end table close square brackets space open square brackets table row 1 cell space 2 end cell row cell negative 2 end cell cell space 1 end cell end table close square brackets equals space open square brackets table row cell 1 minus 4 end cell cell space 2 plus 2 end cell row cell negative 2 minus 2 end cell cell space space minus 4 plus 1 end cell end table close square brackets equals open square brackets table row cell negative 3 space end cell cell space space 4 end cell row cell negative 4 end cell cell negative 3 end cell end table close square brackets space straight B squared space equals open square brackets table row 3 cell negative 4 end cell row 4 3 end table close square brackets space open square brackets table row 3 cell negative 4 end cell row 4 cell 3 space end cell end table close square brackets equals space open square brackets table row cell 3 plus 8 end cell cell negative 4 plus 6 end cell row cell negative 6 plus 4 end cell cell 8 plus 3 end cell end table close square brackets equals space open square brackets table row 11 cell space space 2 end cell row cell negative 2 end cell 11 end table close square brackets therefore space space space 2 AB equals space open square brackets table row 22 cell space 4 end cell row 4 cell space space 22 end cell end table close square brackets therefore space straight A squared plus straight B squared plus 2 AB equals space open square brackets table row cell negative 3 end cell cell space space space 4 end cell row cell negative 4 end cell cell negative 3 end cell end table close square brackets plus open square brackets table row cell negative 7 end cell cell negative 24 end cell row 24 cell negative 3 end cell end table close square brackets plus open square brackets table row 22 4 row 4 22 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets table row cell negative 3 minus 7 plus 22 end cell cell 4 minus 24 plus 4 end cell row cell negative 4 plus 24 minus 4 end cell cell negative 3 minus 7 plus 22 end cell end table close square brackets space space space space space therefore space space space straight A squared plus straight B to the power of 2 plus end exponent 2 space AB equals open square brackets table row 12 cell negative 16 end cell row 16 12 end table close square brackets space space space space space space space space space space space space.... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis. space we space get comma space left parenthesis straight A space plus space straight B right parenthesis squared space equals space straight A to the power of 2 space end exponent plus space 2 space AB space plus space straight B squared

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