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Short Answer Type

131. Give example to show that .
AB = O = BA where A ≠ O, B ≠ O

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132. Give example to show that .
AB = AC but B ≠ C.

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133. Give example to show that
(A + B)² = A² + B² + 2 AB.

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134.

If space straight A equals open square brackets table row 1 2 row 2 1 end table close square brackets comma space then space show space that space space space straight A squared space – space 3 space straight I space equals space 2 straight A.

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135.

If space space straight A equals open square brackets table row 2 3 row 1 cell 2 space end cell end table close square brackets comma space prove space that space straight A to the power of 1 space — space 4 straight A squared space plus space straight A space equals space straight O.

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136.

If space space space straight A equals space open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets

, verify that A² — 5A + 71 = O.

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137.

If space straight A equals space open square brackets table row 3 cell negative 5 end cell row cell negative 4 end cell 2 end table close square brackets space comma

Show that

straight A squared minus 5 straight A minus 141 equals 0

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138.

If space straight A equals space space open square brackets table row 3 cell space space space 2 end cell cell space space 0 end cell row 1 cell space space 4 end cell cell space space 0 end cell row 0 cell space space space 0 space end cell 5 end table close square brackets space comma space show space that space straight A squared space minus 7 straight A space plus space 10 space straight I subscript 3 space end subscript equals space 0

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139. $Find space straight A squared space minus 5 straight A plus 6 space straight I space If space straight A space equals space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets$

Here space space straight A space equals space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets straight A squared space equals space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets space space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets space space equals space open square brackets table row cell 4 plus 0 plus 1 end cell cell 0 plus 0 minus 1 end cell cell 2 plus 0 plus 0 end cell row cell 4 plus 2 plus 3 end cell cell space space space 0 plus 1 minus 3 space space space end cell cell 2 plus 3 plus 0 end cell row cell 2 minus 2 plus 0 end cell cell 0 minus 1 minus 0 end cell cell 1 minus 3 plus 0 end cell end table close square brackets space equals space open square brackets table row 5 cell space space minus 1 end cell cell space space space 2 end cell row 9 cell space space minus 2 end cell cell space space space 5 end cell row 0 cell space minus 1 end cell cell space minus 2 end cell end table close square brackets therefore space straight A squared space minus 5 straight A plus 61 space equals space open square brackets table row 5 cell space space minus 1 end cell cell space space space 2 end cell row 9 cell space space minus 2 end cell cell space space space 5 end cell row 0 cell space minus 1 end cell cell space minus 2 end cell end table close square brackets space minus 5 space space space open square brackets table row 2 0 1 row 2 1 3 row 1 cell negative 1 end cell 0 end table close square brackets space space plus 6 space open square brackets table row 1 cell space 0 end cell cell space 0 end cell row 0 cell space 1 end cell cell space space 0 end cell row 0 cell space 0 end cell cell space 1 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 space space space space space space space space space equals space open square brackets table row 5 cell space space minus 1 end cell cell space space space 2 end cell row 9 cell space space minus 2 end cell cell space space space 5 end cell row 0 cell space minus 1 end cell cell space minus 2 end cell end table close square brackets space space plus space open square brackets table row cell negative 10 end cell cell space space space space 0 end cell cell space space minus 5 end cell row cell negative 10 end cell cell space space minus 5 space space end cell cell negative 15 end cell row cell negative 5 end cell cell space space space 5 end cell cell space space space 0 end cell end table close square brackets space space plus space open square brackets table row 6 cell space space space 0 end cell cell space space 0 end cell row 0 cell space space space 6 space end cell cell space space 0 end cell row 0 cell space space space 0 end cell cell space space 6 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 space space space space space space space space equals space space open square brackets table row cell 5 minus 10 plus 6 end cell cell space space space minus 1 plus 0 plus 0 end cell cell space space space space space space space 2 minus 5 plus 0 end cell row cell 9 minus 10 plus 0 space space end cell cell space space space minus 2 minus 5 plus 6 end cell cell space space space space space space space 5 minus 15 plus 0 end cell row cell 0 minus 5 plus 0 end cell cell space space space space minus 1 plus 5 plus 0 end cell cell space space space space space minus 2 plus 0 plus 6 end cell end table close square brackets space equals space open square brackets table row 1 cell negative 1 end cell cell negative 3 end cell row cell negative 1 end cell cell negative 1 end cell cell negative 10 end cell row cell negative 5 end cell 4 4 end table close square brackets

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140.

If space straight A equals space open square brackets table row 1 2 row 2 1 end table close square brackets space comma space straight f space left parenthesis straight x right parenthesis space equals straight x to the power of 2 space end exponent minus 2 straight x minus 3 space show space that space straight f left parenthesis straight A right parenthesis equals straight O

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