Matrices

If A = $\left[\begin{array}{cc}\mathrm{x}& - 2\\ 3& 7\end{array}\right]$ and A^{- 1} = $\left[\begin{array}{cc}\frac{7}{34}& \frac{1}{17}\\ \frac{- 3}{34}& \frac{2}{17}\end{array}\right]$, then the value of x is

• 2

• 3

• - 4

• 4

If $\left|\begin{array}{ccc}{\mathrm{x}}^2 + \mathrm{x}& 3\mathrm{x} - 1& - \mathrm{x} + 3\\ 2\mathrm{x} + 1& 2 + {\mathrm{x}}^2& {\mathrm{x}}^3 - 3\\ \mathrm{x} - 3& {\mathrm{x}}^2 + 4& 3\mathrm{x}\end{array}\right|$ = ${\mathrm{a}}_{0 }+ {\mathrm{a}}_1\mathrm{x} + {\mathrm{a}}_2{\mathrm{x}}^2 + ... + {\mathrm{a}}_7{\mathrm{x}}^7$, then the value of a₀ is

• 25

• 24

• 23

• 21

If A is a non-singular matrix of order 3, then adj (adj A) is equal to

• A

• A^{- 1}

• $\frac{1}{\left|\mathrm{A}\right|}\mathrm{A}$

• $\left|\mathrm{A}\right|\mathrm{A}$

If $\left[\begin{array}{c}\mathrm{x} - \mathrm{y} - \mathrm{z}\\ - \mathrm{y} +\hspace{0.17em}\mathrm{z}\\ \mathrm{z}\end{array}\right] = \left[\begin{array}{c}0\\ 5\\ 3\end{array}\right]$, then the value of x, y and z are respectively

• 5, 2, 2

• 1, - 2, 3

• 0, - 3, 3

• 11, 8, 3

Which one of the following is true always for any two non-singular matrices A and B of same order ?

• AB = BA

• (AB)^t = A^tB^t

• (A + B)(A - B) = A² - B²

• (AB)^{- 1} = B^{- 1}A^{- 1}

If A = $\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& - 2\\ \mathrm{a}& 2& \mathrm{b}\end{array}\right]$ is a matrix satisfying AA^T = 9I₃, then the values of a and b are respectively.

• 1, 2

• - 1, 2

• - 1, - 2

• - 2, - 1

If A = $\left[\begin{array}{cc}2& 1\\ 0& \mathrm{x}\end{array}\right]$ and A^{- 1} = $\left[\begin{array}{cc}\frac{1}{2}& \frac{1}{6}\\ 0& \frac{1}{\mathrm{x}}\end{array}\right]$, then the value of x is equal to

• - 3

• 3

• - 2

• 6

If A = $\left(\begin{array}{cc}\cos \left(\mathrm{\alpha }\right)& \sin \left(\mathrm{\alpha }\right)\\ \sin \left(\mathrm{\alpha }\right)& \cos \left(\mathrm{\alpha }\right)\end{array}\right)$, then A¹⁰ is equal to

• $\left(\begin{array}{cc}{\cos }^{10}\left(\mathrm{\alpha }\right)& {\sin }^{10}\left(\mathrm{\alpha }\right)\\ - {\sin }^{10}\left(\mathrm{\alpha }\right)& {\cos }^{10}\left(\mathrm{\alpha }\right)\end{array}\right)$

• $\left(\begin{array}{cc}{\cos }^{10}\left(\mathrm{\alpha }\right)& - {\sin }^{10}\left(\mathrm{\alpha }\right)\\ {\sin }^{10}\left(\mathrm{\alpha }\right)& {\cos }^{10}\left(\mathrm{\alpha }\right)\end{array}\right)$

• $\left(\begin{array}{cc}{\cos }^{10}\left(\mathrm{\alpha }\right)& {\sin }^{10}\left(\mathrm{\alpha }\right)\\ - {\sin }^{10}\left(\mathrm{\alpha }\right)& - {\cos }^{10}\left(\mathrm{\alpha }\right)\end{array}\right)$

• $\left(\begin{array}{cc}\cos \left(10\mathrm{\alpha }\right)& \sin \left(10\mathrm{\alpha }\right)\\ - \sin \left(10\mathrm{\alpha }\right)& \cos \left(10\mathrm{\alpha }\right)\end{array}\right)$

If A = $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ \mathrm{a}& \mathrm{b}& - 1\end{array}\right]$ and I is the unit matrix of order 3, then A² + 2A⁴ + 4A⁶ is equal to

• 7 A⁸

• 7 A⁷

• 8 I

• 6 I

If A = $\left[\begin{array}{cc}\mathrm{x}& 1\\ 1& 0\end{array}\right]$  and A² is the unit matrix, then the value of x³ + x - 2 is equal to

• - 8

• - 2

• 0

• 1