# Matrices: $$A\neq I$$ and $$A^2=I$$

Algebra Level 4

$A=\frac{1}{5}\left(\begin{array}{cc} -3& a\\b& c \end{array}\right)\qquad \text{and}\qquad \, A^2=\left(\begin{array}{cc} 1& 0\\0& 1 \end{array}\right)$

Given that $$a, b$$ and $$c$$ are integers satisfying the constraints above, find the maximum value of $$a+b+c$$.

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