If inverse of the matrix $\left[\begin{array}{cc}2 & -0.5 \\ -1 & x\end{array}\right]$ is $\left[\begin{array}{ll}1 & 1 \\ 2 & 4 \end{array}\right]$, then the value of $x$ is

If a $3 \times 3$ matrix is filled with +1's and -1's such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is

If $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]$, then the absolute value of the determinant of $\left(A^{9}+A^{6}+A^{3}+A\right)$ is __________.

If $A$ is a $3 \times 3$ non-zero matrix such that $A^2 = 0$ then the determinant of $(I + A)^{50} - 50A$ is equal to

If $A, B$ and $A + B$ are non singular matrices and $AB = BA$ then $2A - B - A(A + B)^{-1}A + B(A + B)^{-1} B$ equals

If $A=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 0\end{array}\right]$ then $A^{2022}$ is

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then the determinant of $A + A^2 + A^3 + \cdots + A^{13}$ is