If $A$ is a square matrix such that $A^2=I$, then $(A-I)^3+(A+I)^3-7 A$ is equal to

For any two matrices $A$ and $B$, we have

Q. 66 On using elementary column operations $C_2 \rightarrow C_2-2 C_1$ in the following matrix equation $\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]$, we have

On using elementary row operation $R_1 \rightarrow R_1-3 R_2$ in the following matrix equation $\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$, we have

........... matrix is both symmetric and skew-symmetric matrix.