Which of the following statements are correct ?

A. If the product of 2 non-zero square matrices is a zero matrix, then either A is singular or B is singular

B. If A is a non singular matrix , then $|A^{-1}| = \dfrac{1}{|A|}$

C. If A is an invertible square matrix then $adj\,A^T = \dfrac{1}{adj\,A}$

D. If A and B are invertible matrices then $(AB)^{-1} = B^{-1}A^{-1}$

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If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to

For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$, then $\lvert 4\,adj A\rvert$ is equal to

If A and B are invertible matrices of the same order, then

Match List-I with List-II

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If $M = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$ and $N = [7 \quad 1 \quad -4]$, then $(MN)^T$ will be equal to:

Let A be a matrix such that $A = \begin{bmatrix} 1 & 2 \\ -2 & 3 \end{bmatrix}$. Then which of the following are TRUE?

(A) A is non-singular matrix

(B) $A^T = A$

(C) A is not invertible matrix

(D) A is not skew-symmetric matrix

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If $A$ is a square matrix of order 3 such that $A(adj\,A)=\begin{bmatrix}-3 & 0 & 0\\0 & -3 & 0\\0 & 0 & -3\end{bmatrix}$, then which of the following is NOT correct?