If $A = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix}$, then $A^3 - A^2$ is equal to

If the matrix $\left[\begin{array}{rr}2 & 3 \\ 5 & -1\end{array}\right]=A+B$,where $A$ is symmetric and $B$ is skew-symmetric,then $B$ is equal to

If $A=\begin{bmatrix} 1 & 1 \\ 0 & i \end{bmatrix}$ and $A^{2018}=\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, then $(a+d)$ equals

For matrix $A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$, if $A^2 - 2I = KA$, then $K = \dots$

Assuming that the sums and products given below are defined,which of the following is not true for matrices?

Let $M$ be a $3 \times 3$ matrix satisfying $M\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \\ 3 \end{bmatrix}$,$M\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix}$,and $M\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 12 \end{bmatrix}$. Then the sum of the diagonal entries of $M$ is