Matrices & Systems · Hard problem

A $2\times2$ calibration matrix $A = \begin{pmatrix}a & 2\\3 & b\end{pmatrix}$ has two unknown constants $a, b$. Multiplying $A$ by a known test matrix $B = \begin{pmatrix}1 & 4\\2 & 1\end{pmatrix}$ should reproduce the known reference matrix $AB = \begin{pmatrix}7 & 14\\13 & 17\end{pmatrix}$. Find $a+b$.