\text { The eigenpairs }=\text { (eigenvalue, eigenvector) of matrix } \mathbf{A} \text { are }\left(8,[2,1]^{T}\right) \text { and }\left(3,[3,2]^{T}\right) \text {. } What is matrix A?

\text { Calculate } \mathbf{A}^{5} \text { using the eigenvalue decomposition (diagonalization) } \mathbf{A}=\mathbf{P D P}^{-1} \text { when } A=\left[\begin{array}{cc}

-7 & 2 \\

2 & -10

\end{array}\right] \text { Also give the eigenvalues } \lambda_{1} \text { and } \lambda_{2} \text {. }