Let $A$ and $B$ be two non-singular, square matrices of same order, and

A. $(AB)^{-1} = B^{-1} \cdot A^{-1}$

B. $(A+B)^{-1} = B^{-1} + A^{-1}$

C. $adj. A = |A| \cdot A^{-1}$

D. $det(A^{-1}) = [det A]^{-1}$

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Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$

(D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$

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If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to

If $A = \begin{bmatrix}0 & x^2-6 & -3\\-x & 0 & -8\\x^2-2x & 8 & 0\end{bmatrix}$ is a skew symmetric matrix, then the value(s) of x is/ are -

(A) 3

(B) -3

(C) -2

(D) -1

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If the points (2, 1), $(-1, 4)$ and (a, 3) are collinear then the value/(s) of a is/(are) :

If $A=\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}-2 & 3\\1 & 2\end{bmatrix}$ such that $2B-3A+X=0$ then $X$ is

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