If $A$ is a square matrix of order $n \times n$, then which of the following are correct?

(A) $|kA| = k^n|A|$, $k$ is a constant

(B) $|k\ adjA| = k^n|adjA|^{n-1}$, $k$ is a constant

(C) $|adj\ adjA| = |A|^{(n-1)^2}$

(D) $A(adjA) = |A|I$, $I$ is an identity matrix of order $n$

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If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then

Match List-I with List-II

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Which of the following statements are correct?

A. If $P$ and $Q$ are square matrices of same order, then $(PQ^T-QP^T)$ is a skew symmetric matrix.

B. The number of all possible matrices of order $3\times2$ with each entry either –1 or 1, is 64.

C. If $P$ is an invertible matrix, then $P^T$ is also invertible.

D. If $P$ and $Q$ are square matrices of the same order, then $|PQ|=|P|+|Q|$.

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If $A = [a_{ij}]_{3 \times 3}$ and $a_{ij} = i - j$, then which of the following statements are TRUE?

(A). $A$ is scalar matrix

(B). $A$ is skew symmetric matrix

(C). $|A| = 0$

(D). $a_{21} + a_{12} = 0$

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If A and B are square matrices of order n, such that AB = A and BA = B, then $A^2$ =

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

If $A = \begin{bmatrix}0 & x & 3\\2 & y & -1\\z & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then the value of $3x+y-2z$ is