If $(AB)^T = C$, where $A = \begin{bmatrix} x & -1 \\ 2 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 5 \\ 1 & -2 \end{bmatrix}$ and $C = \begin{bmatrix} 3 & 11 \\ 7 & y \end{bmatrix}$, then $x+y$ is :

If $\begin{vmatrix} 2x & 2 \\ 4 & x \end{vmatrix} = 10$, then $x$ is:

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 $A^2 = 8A + kI, A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then value of $k$ is:

Let $A$ be a non singular matrix of order $n \times n$, Then $|\text{adj }(3A)|$ is equal to:

If A and B are symmetric matrices of the same order, then which one of the following is true?

Let $A$ be a matrix given by $A=[a_{ij}]_{3\times3}$, $a_{ij}=i+j$, then

Match List-I with List-II

Choose the correct answer from the options given below: