Problem $1(10$ points$)$

Given a matrix $A=\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]$ and a vector $B=\left[\begin{array}{c}1\\ 2\end{array}\right]$ find:

a$.A^T$

b$.A^{-1}$

c$.B^{T}B$

d$.B{B}^T$

e$.AB$

f$.$ Eigenvalues of $A$

g$.$ Eigenvectors of $A$