If A and B are square matrices of order n, such that AB = A and BA = B, then $A^2$ =

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

$A = \begin{bmatrix} 1/3 & 2 \\ 0 & 2x - 3 \end{bmatrix}$ & $B = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$ If $AB = I$ (Where I is an identity matrix of order 2) , then value of x is

$A=\begin{bmatrix} 0 & 1 & 3 \\ 1 & 2 & x \\ 2 & 3 & 1 \end{bmatrix}$ and $2B=\begin{bmatrix} 1 & -8 & 5 \\ -1 & 6 & -3 \\ 1 & 2y & 1 \end{bmatrix}$. If $A=B^{-1}$ then $x+y$ is equal to

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

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

If $\begin{vmatrix} 1 & x & x^2 \\ x^2 & 1 & x \\ x & x^2 & 1 \end{vmatrix} = (x^{\lambda}-1)^{\mu}$ then the value of $\lambda$ and $\mu$ are given by