Let P and Q be any two invertible matrices of the same order. Then

Match List-I with List-II

List-I	List-II
Matrix	Equivalent matrix
(A) $(P Q)^{-1}$	(I) $Q^{-1}P$
(B) $(P^{-1}Q)^{-1}$	(II) $Q P^{-1}$
(C) $(P Q^{-1})^{-1}$	(III) $Q^{-1}P^{-1}$
(D) $(P^{-1}Q^{-1})^{-1}$	(IV) Q P

Choose the correct answer from the options given below:

For a square matrix $A = \begin{bmatrix} 2 & 1 & 3 \\ 0 & -1 & 4 \\ 1 & 2 & 0 \end{bmatrix}$, which of the following statements is/are TRUE ?

A. det (A) = 9.

B. $A_{21}.A_{33} = -12$, where $A_{ij}$ is the cofactor of $a_{ij}$

C. det (A) = $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{31}$.

D. $\lvert AA'\rvert \neq \lvert A\rvert^2$

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The value (/s) of $x$ satisfying the matrix equation:

$x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\10 & 6x\end{bmatrix}$ is/are:

If $\begin{bmatrix}3 & 1\\2 & 1\end{bmatrix}A\begin{bmatrix}2 & 1\\1 & 1\end{bmatrix} = \begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}$, then matrix 'A' is

If $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals

A matrix which is both symmetric and skew symmetric is a

If $A$ is a square matrix of order 3 such that $|A|=3$, then the value of $|adj(adjA)|$ is equal to