Answer
$$A^T=\left[\begin{array}{rrr}{3} & {2} \\ {-1} & {0} \end{array}\right].$$
$$A^TA=\left[\begin{array}{rrr}{13} & {-3} \\ {-3} & {1} \end{array}\right].$$
$$AA^T=\left[\begin{array}{rrr}{10} & {6} \\ {6} & {4} \end{array}\right].$$
Work Step by Step
Let $A$ be given by
$$A=\left[\begin{array}{rrr}{3} & {-1} \\ {2} & {0} \end{array}\right].$$
Now, we have
$$A^T=\left[\begin{array}{rrr}{3} & {2} \\ {-1} & {0} \end{array}\right].$$
$$A^TA=\left[\begin{array}{rrr}{3} & {2} \\ {-1} & {0} \end{array}\right]\left[\begin{array}{rrr}{3} & {-1} \\ {2} & {0} \end{array}\right]=\left[\begin{array}{rrr}{13} & {-3} \\ {-3} & {1} \end{array}\right].$$
$$AA^T=\left[\begin{array}{rrr}{3} & {-1} \\ {2} & {0} \end{array}\right]\left[\begin{array}{rrr}{3} & {2} \\ {-1} & {0} \end{array}\right]=\left[\begin{array}{rrr}{10} & {6} \\ {6} & {4} \end{array}\right].$$
