If $A =\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \;adj A = AA^T$, then $5a+b$ is equal to

Question

$\begin{array}{1 1}(1) -1 \\ (2) 5 \\ (3) 4 \\ (4) 13 \end{array} $