Determinant of Square Matrix

If $A$ and $B$ are square matrices of order $n$, then $A-\lambda I$ and $B-\lambda I$ commute for every scalar $\lambda$, only if

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ a& 2& b\end{array}\right]$ is a matrix satisfying the equation $A{A}^T=9I,$where, $I$ is $3\times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

Let $A$ be a square matrix of order $3$ satisfies the relation $A^3-6A^2+7A-8I=O$ and $B=A-2I$ . Also, $\det \left(A\right)=8$ , then 

If $D_1$ and $D_2$ are two $3\times 3$ diagonal matrices, then which of the following is/are true?