If $A=\begin{bmatrix}a & 0\\0 & 0\end{bmatrix}$ and $B=\begin{bmatrix}0 & 0\\0 & b\end{bmatrix}$ then the matrix $A^3B^3$ is:

If $P = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} 4 & 0 \\ 1 & 5 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 0 \\ 1 & -2 \end{bmatrix}$, then which of the following are TRUE?

(A) $(P^T)^T = P^T$

(B) $(P-Q)R = PR - QR$

(C) $(P-Q)^T = Q^T - P^T$

(D) $(PQ)^T = Q^TP^T$

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If A and B are invertible matrices of same order, then which one of the following is NOT true?

If $A$ is an invertible matrix of order 3, then

Match List-I with List-II

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If the matrix $\begin{bmatrix} z & x-y+2 & x+4y-3 \\ x+y & 0 & a-3 \\ 2x-y+3 & a-1 & 0 \end{bmatrix}$ is skew-symmetric, then the value of $(a+x+y+z)$ is:

Let $A$ be a non-singular square matrix of order $n$, then

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If matrix A is of order $2 \times 3$ and B of order $3 \times 2$, then