Matrices & Systems · Hard problem

An encoding scheme pre-multiplies a secret key matrix $X$ by $A = \begin{pmatrix}1 & 2\\0 & 1\end{pmatrix}$ and post-multiplies by $B = \begin{pmatrix}2 & 0\\1 & 1\end{pmatrix}$, producing the matrix $AXB$. A cryptanalyst, who already knows $A$ and $B$, intercepts $AXB = \begin{pmatrix}17 & 7\\7 & 3\end{pmatrix}$. Find the sum of all four entries of the secret key matrix $X$.