Let $A$ be a non-singular square matrix of order $n$, then Match List-I with List-II | List-I | List-II | | --- | --- | | (A) $A(\text{adj} A)$ | (I) $\frac{1}{\vert A\vert }$ | | (B) $\vert \text{adj} A\vert $ | (II) $\vert A\vert ^n$ | | (C) $\vert A^{-1}\vert $ | (III) $\vert A\vert I$ | | (D) $\vert A(\text{adj} A)\vert $ | (IV) $\vert A\vert ^{n-1}$ | Choose the correct answer from the options given below:

If $A = \begin{bmatrix}2 & 3 & 1 \\ 2 & -1 & 0\end{bmatrix}$ and $B^T = \begin{bmatrix}4 & 4 \\ 6 & -2 \\ 2 & 0\end{bmatrix}$, then $4A + B$ is

If matrix $A = \begin{bmatrix} x & 2 & 3 \\ a & y & -5 \\ b & c & 0 \end{bmatrix}$ is a skew-symmetric matrix, then

(A) $x + y + c = 5$

(B) $c = 5$

(C) $a + b + c = 0$

(D) $a + b - c = 10$

Choose the correct answer from the options given below:

If $\begin{vmatrix}4x & 9\\ -4 & -5\end{vmatrix}=\begin{vmatrix}4 & 8\\ 2 & 3\end{vmatrix}$, then the value of $x$ is :

If $A = \begin{bmatrix} 1 & -2 & 3 \\ -4 & 2 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -2 \\ 3 & -4 \\ 2 & 4 \end{bmatrix}$ then product AB is :

Suppose that A, B and C are matrices of order $m \times n$, $n \times 5$ and $5 \times q$ respectively. The restriction on $m$, $n$ and $q$ so that AB-BC is defined are

If $A = \begin{bmatrix} 0 & 0 & \sqrt{3} \\ 0 & \sqrt{3} & 0 \\ \sqrt{3} & 0 & 0 \end{bmatrix}$, then $|adj A|$ is equal to