Match List-I with List-II

List-I	List-II
Matrix A	$\left\vert \text{adj}A \right\vert$
(A) $\begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$	(I) $2$
(B) $\begin{bmatrix} 3 & 0 \\ 1 & 5 \end{bmatrix}$	(II) $5$
(C) $\begin{bmatrix} 6 & -1 \\ 5 & 3 \end{bmatrix}$	(III) $15$
(D) $\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$	(IV) $23$

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The value of $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix}$ is:

Which of the following statement is/are correct?

(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$

(B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$

(C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i, j$

(D) The multiplication of diagonal matrices of same order is commutative

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Match List-I with List-II

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The value of $\begin{vmatrix}x & a & a\\a & x & a\\a & a & x\end{vmatrix}$ is equal to:

If $A$ is a square matrix such that $|A| \neq 0$ and $A^2 - A + 2I = 0$ then $A^{-1}$ is equal to :(where $I$ is an identity matrix of order as order of matrix $A$)

Let $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -6 \\ -2 & 4 \end{bmatrix}$

(A) $\det(A^T) = 1$

(B) $AB = I$, where $I$ is the identity matrix of order 2.

(C) $A^{-1} = \begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$

(D) adj $(B) = \begin{bmatrix} 4 & 2 \\ 6 & 4 \end{bmatrix}$

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