If $A=\begin{bmatrix} 0 & -\tan\alpha/2 \\ \tan\alpha/2 & 0 \end{bmatrix}$, then the value of $\begin{bmatrix} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{bmatrix}$ for all $\alpha \in \mathbb{R}$(set of real numbers), is

(I is identity matrix of order 2)

If P, Q and R are matrices of order 2x3, 3x5 and 5x3 respectively. Then which of the following are valid?

(A) P Q R

(B) P R Q

(C) Q R

(D) R Q

(E) P R

Choose the correct answer from the options given below:

If $A$ is a $3 \times 3$ matrix such that $|adj A| = 9$ and $|kA^{-1}| = 9$, then the value of $k$ are:

Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$.

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

Choose the correct answer from the options given below:

If $A$ and $B$ are invertible matrices of order $3$ then match List-I with List-II

Choose the correct answer from the options given below:

If $A$ is a square matrix and $I$ is an identity matrix such that $A^{2}=A$, then $A(I-2 A)^{3}+2 A^{3}$ is equal to :

The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively: