Determinants & Inverses · Medium problem

A budget tracker records quarterly amounts for three expense categories as the rows of $M=\begin{pmatrix}2&3&5\\1&1&2\\4&5&9\end{pmatrix}$. An auditor suspects category $C$'s row is fully explained as a combination of categories $A$ and $B$ (so $\det M=0$, confirmed). The Q3 entry for category $C$ (currently $9$) was recorded sloppily; find the smallest positive integer amount by which it must be increased for the three categories to stop being redundant (i.e. for $\det M$ to become nonzero).