Let \(a,b,c\) be integers such that \(\mathbf{A} = \frac{1}{5} \begin{pmatrix} -3 & a \\ b & c \end{pmatrix}\)
and \(\mathbf{A}^2 = \mathbf{I}\) Find the largest possible value of \(a+b+c\)
The largest possible value of a + b + c is 29.
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+22 
