$A$ square matrix $P$ satisfies $P^2 = I - P$. If $P^n = 5I - 8P$,then $n$ is:

For $3 \times 3$ matrices $M$ and $N$,which of the following statement$(s)$ is (are) $NOT$ correct?

Let $M$ and $N$ be two $3 \times 3$ non-singular skew-symmetric matrices such that $MN = NM$. If $P^T$ denotes the transpose of $P$,then $M^2 N^2 (M^T N)^{-1} (M N^{-1})^T$ is equal to

Matrix $A$ satisfies $A^2 = 2A - I$,where $I$ is the identity matrix. Then for $n \ge 2$,$A^n$ is equal to $(n \in N)$:

$A$ and $B$ are two non-singular square matrices of order $3 \times 3$ such that $AB = A$ and $|A + B| \neq 0$. Then:

If $AA^T = I$ and $C$ is a skew-symmetric matrix,then $((A^T CA)^{50})^T$ is equal to