Which of the following statements are TRUE?

A. If the product of two matrices is a zero matrix, it is not necessary that one of the matrix is a zero matrix.

B. For any three matrices A, B and C, $(AB)C = A(CB)$.

C. Diagonal elements of a skew symmetric matrix can be non-zero.

D. Multiplication of diagonal matrices of same order is always commutative.

Choose the correct answer from the options given below:

Which of the following statements is incorrect regarding matrices ?

For any matrices A and B of suitable orders,

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 $|PQ|=|P|+|Q|$.

Choose the correct answer from the options given below:

Let $A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$, then adjoint (A) is:

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

The integral value of k for which the system of linear equations $kx + y + 2z = 0$, $ky = x - 3z$ and $2x + y + kz = 0$ has a non-zero solution is

If $A$ and $B$ square matrices of order 3 such that $|A| = -1$, $|B| = 5$, then the value of $|2AB|$ is: