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:

The number of all possible matrices of order $2 \times 3$ with entries -1 or 1 is

If $A = [a_{ij}]_{3\times3}$ is a square matrix, where $a_{ij} = i - j + 3$, then the value of $a_{21} + a_{31} - a_{23}$ is

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

$\begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}$ is equal to:

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then