If A and B are square matrices of same order, then $A'B - B'A$ is a:

The number of all possible matrices of order $3 \times 3$ with each entry $-1, 0$ or $1$ is

The real value of $a$ for which the system of equations $x+ay=0, y+az=0, z+ax=0$ has infinitely many solutions, is :

Let A = PQ. The elementary operation on A, that produces the same effect as it does on applying on P and keeping Q unchanged is :

(A) $R_i \leftrightarrow R_j$

(B) $R_i \to R_i + KR_j$

(C) $C_i \to KC_i$

(D) $C_i \to C_i + KC_j$

Choose the correct answer from the options given below :

The number of all possible matrices of order 3 x 3 with each entry belonging to the set {0, 1} is:

If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then

Which of the following matrices are diagonal matrices?

A. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$

B. $\begin{bmatrix} 1 & 2 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}$

C. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

D. $\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}$

Choose the correct answer from the options given below: