Inverse of a diagonal non-singular matrix is

diagonal matrix

zero matrix

skew symmetric matrix

scalar matrix

If A is 3 x 4 matrix and B is a matrix such that A’B and BA’ are both defined, then B is of the type

4 x 4

3 x 4

4 x 3

3 x 3

The value of \(\large sin^{-1}\left ( \frac{2\sqrt{2}}{3} \right )+sin^{-1}\left ( \frac{1}{3} \right )\) is equal to

\(\large \frac{\pi }{6}\)

\(\large \frac{\pi }{2}\)

\(\large \frac{\pi }{4}\)

\(\large \frac{2\pi }{3}\)

The inverse of the matrix \(\large \begin{bmatrix} 1\: \:\; \; 0\: \:\; \; 0 \\ 3\: \:\; \; 3\: \:\; \; 0 \\ 5\: \: 2\: \: -1 \end{bmatrix}\) is

\(\large -\frac{1}{3} \begin{bmatrix} -3\: \:\; \; 0\: \:\; \; 0 \\ 3\: \:\; \; 1\: \:\; \; 0 \\ 9\: \: 2\: \: -3 \end{bmatrix}\)

\(\large -\frac{1}{3} \begin{bmatrix} -3\: \:\; \; 0\: \:\; \; 0 \\ 3\: \:\; \; -1\: \:\; \; 0 \\ - 9\: \: -2\: \: 3 \end{bmatrix}\)

\(\large -\frac{1}{3} \begin{bmatrix} 3\: \;\:\; \; \; 0\: \:\; \; \;\; 0 \\ 3\: \:\; \; -1\: \:\; \; 0 \\ - 9\: \: -2\: \: 3 \end{bmatrix}\)

\(\large -\frac{1}{3} \begin{bmatrix} -3\: \:\; \;\: \:\: \: 0\: \:\; \;\: \: 0 \\ -3\: \:\; \; -1\: \:\; \; 0 \\ -9\: \: \:\: -2\: \:\: \: 3 \end{bmatrix}\)

If \(\large A=\begin{bmatrix} cos\theta &\; \; \; sin\theta \\ -sin\theta &\; \; \; cos\theta \end{bmatrix}\), then A. A' is ...........................

A

-A

\(\large A^{2}\)

I

If \(\large \begin{bmatrix} 1 &\; \; 2 &\; \; -1 \\ 1&\; \; x-2 &\; \; 1 \\ x&\; \; 1 & \; \; 1 \end{bmatrix}\) is singular, then the value of x is ………

3

1

0

2

If A and B are symmetric matrices of the same order, then which one of the following is NOT true?

AB – BA is symmetric

A + B is symmetric

A – B is symmetric

AB + BA is symmetric

\(\large G = \left \{ \begin{bmatrix} \times & \times \\ \times & \times \end{bmatrix}, \times \;is \; a\; nonzeroreal\; number \right \}\)is is a group with respect to matrix multiplication. In this group, the inverse of \(\large \begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\ \frac{1}{3}&\frac{1}{3} \end{bmatrix}\) is..........................

\(\large \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}\)

\(\large \begin{bmatrix} \frac{4}{3} & \frac{4}{3} \\ \frac{4}{3} & \frac{4}{3} \end{bmatrix}\)

\(\large \begin{bmatrix} \frac{3}{4} & \frac{3}{4} \\ \frac{3}{4} & \frac{3}{4} \end{bmatrix}\)

\(\large \begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}\)

The characteristic equation of a matrix A is \(\large \lambda^3 -5\lambda^2-3\lambda+2=0\) then \(\large \left | adj(A) \right | =\)

4

\(\large \frac{1}{2}\)

25

9

If A and B have n elements in common, then the number of elements common to A x B and B x A is

2n

n

0

n\(\large ^{2}\)

If A and B are square matrices of order ‘n’ such that A\(\large ^{2}\) – B\(\large ^{2}\) = (A – B) (A + B), then which of the following will be true?

Either of A or B is zero matrix

A = B

AB = BA

Either of A or B is an identity matrix

If the matrix \(\large \left | \begin{matrix} 2\: \: \:\: \: 3\\ 5\: -1 \end{matrix} \right |\)  = A + B, where A is symmetric and B is skew symmetric, then B = ….

\(\large \left | \begin{matrix} 2\: \: \:\: \: 4\\ 4\: -1 \end{matrix} \right |\)

\(\large \left | \begin{matrix} 0\: -2\\ 2\: \: \; \; \: 0 \end{matrix} \right |\)

\(\large \left | \begin{matrix} 0\: \: \: \: 1\\ -1 \: \; \; 0 \end{matrix} \right |\)

\(\large \left | \begin{matrix} 0\: \: - 1\\ 1 \: \; \; \: \: 0 \end{matrix} \right |\)

If  \(\large 2x\: \: =\: -1+\sqrt{3}I,\) then the value of \(\large \left ( 1+x^{2}+x \right )^{6}-\: \: \left ( 1-x+x^{2} \right )^{6}=.........\)

32

64

-64

0

The symmetric part of the matrix \(\large A=\begin{pmatrix} 1 & 2 & 4\\ 6 & 8 & 2\\ 2 & -2 &7 \end{pmatrix} is\)

\(\large \begin{pmatrix} 0 & -2 & -1\\ -2 & 0 & -2\\ -1 & -2 &0 \end{pmatrix}\)

\(\large \begin{pmatrix} 1 & 4 & 3\\ 2 & 8 & 0\\ 3 & 0 & 7 \end{pmatrix}\)

\(\large \begin{pmatrix} 0 & -2 & -1\\ 2 & 0 & 2\\ -1 & 2 & 0 \end{pmatrix}\)

\(\large \begin{pmatrix} 1 & 4 & 3\\ 4 & 8 & 0\\ 3 & 0 & 7 \end{pmatrix}\)

If A is a matrix of order 3, such that A (adj A) = 10 I, then |adj A| =

1

10

100

10 I

The inverse of the matrix \(\large A = \begin{pmatrix} 2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 4 \end{pmatrix}\) is

\(\large \frac{1}{24}\begin{pmatrix} 2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 4 \end{pmatrix}\)

\(\large \begin{pmatrix} 2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 4 \end{pmatrix}\)

\(\large \frac{1}{24}\begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}\)

\(\large \begin{pmatrix} \frac{1}{2} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{4} \end{pmatrix}\)

Solve for x  \(\large tan^{-1}\left (\frac{ 1-x }{ 1+x }\right )=\frac{1}{2}tan^{-1}x,x> 0\) 

\(\large \sqrt{3}\)

1

-1

\(\large \frac{1}{\sqrt{3}}\)

\(\large If \frac{\left ( x+1 \right )^{2}}{x^{3}+x}=\frac{A}{x}+\frac{Bx+C}{x^{2}+1},\) then \(\large cosec^{-1}\left ( \frac{1}{A} \right )+cot^{-1}\frac{1}{B}+sec^{-1}C= \)

\(\large \frac{5\pi }{6}\)

0

\(\large \frac{\pi }{6}\)

\(\large \frac{\pi }{2}\)

If   \(\large A= \begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix}\), then A\(\large ^{2}\) equal to ___

\(\large \begin{bmatrix} 0\; \; 1 & \\ 1\; \; 0& \end{bmatrix}\)

\(\large \begin{bmatrix} 1\; \; 0 & \\ 1\; \; 0& \end{bmatrix}\)

\(\large \begin{bmatrix} 1\; \; 0 & \\ 0\; \; 1& \end{bmatrix}\)

\(\large \begin{bmatrix} 0\; \; 1 & \\ 0\; \; 1& \end{bmatrix}\)

If A = \(\large \begin{bmatrix} \alpha \; \; 2 & \\ 2\; \; \alpha & \end{bmatrix}\) and \(\large \left | A^{3} \right | \) = 27 , then \(\large \alpha \) = _____

\(\large \pm 1\)

\(\large \pm 2\)

\(\large \pm \sqrt{7}\)

\(\large \pm \sqrt{5}\)