If $P = \begin{bmatrix}0 & 1\\ 1 & 1\end{bmatrix}$ and $Q = \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}$, then which of the following are correct?

(A) $P+Q$ is a singular matrix.

(B) $P-Q$ is a symmetric matrix.

(C) $P$ and $Q$ are non-singular matrices.

(D) $(P+Q)(P-Q) \neq P^2 - Q^2$

Choose the correct answer from the options given below:

The matrix which is both symmetric and skew-symmetric, is a:

The set of values of K for which the system of equations $\begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 0 \\ 1 & K & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}$ gives a unique solution is :

If $A$ and $B$ are matrices of the same order, then $AB^T - BA^T$ is a

If the matrix $A = \begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $2x - 3y + 5z$ is equal to

If $\begin{bmatrix} 3 & 2x+5y & -2 \\ x+4y & 7 & -5 \end{bmatrix} = \begin{bmatrix} 3 & 10 & -2 \\ 2 & 7 & -5 \end{bmatrix}$ Then the values of $x$ and $y$ are :

If $A = \begin{bmatrix}1 & -1\\2 & -1\end{bmatrix}, B = \begin{bmatrix}x & 1\\y & -1\end{bmatrix}$ and $(A+B)^2 = A^2 + B^2$, then which of the following are correct?

A. $x=1$

B. $x=4$

C. $y=1$

D. $y=4$

Choose the correct answer from the options given below: