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 the points (a, b), (c, d) and (a + c, b + d) are collinear, then

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 7 \end{bmatrix}$ and $2A^{-1} = KI - A$, where K is a real number and I is the identity matrix of order 2, then the value of K is:

The value of $y$ is

Match List-I with List-II

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Let $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2 \end{bmatrix}$. $M_{ij}$ and $A_{ij}$ respectively denote the minor and cofactor of an element $a_{ij}$ of matrix $A = [a_{ij}]$

(A) $M_{23} = 6$

(B) $A_{22} = -8$

(C) $A_{13} = 7$

(D) $M_{32} = -5$

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Let $A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then which of the following are true?

(A) $|A| = 2 + 2 \sin^{2} \theta$

(B) $|A| = 2 + \sin^{2} \theta$

(C) minimum value of $|A|$ is $1$

(D) maximum value of $|A|$ is $4$

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