For the matrix $A=\begin{bmatrix} 0 & 0 & 5 \\ 0 & 6 & 0 \\ 7 & 0 & 0 \end{bmatrix}$, which of the following statement(s) is/are TRUE ?

A. $A$ is a scalar matrix.

B. $A$ is a diagonal matrix.

C. $A$ is a square matrix.

D. $A$ is a skew symmetric matrix.

Choose the correct answer from the options given below:

Let $A$ and $B$ be two symmetric matrices of same order, then

Match List-I with List-II

Choose the correct answer from the options given below:

If A is a skew-symmetric matrix then, the matrix $B^TAB$ is:-

If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \\ x & 1 & 1 \end{bmatrix}$ and $A^{-1} = \frac{1}{4}\begin{bmatrix} -2 & 0 & y \\ 5 & -2 & -1 \\ 1 & 2 & -1 \end{bmatrix}$, then values of x and y, are:

The value of $\begin{vmatrix} \sqrt{3}/2 & 1/2 \\ \sqrt{3}/2 & 1/2 \end{vmatrix}$

If A and B are two matrices of order 2 × 2 such that A is a symmetric matrix and B is a skew-symmetric matrix, then:

If $A = \begin{bmatrix}0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0\end{bmatrix}$ is a skew-symmetric matrix, then