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Largest sum for an involutory matrix

High school · ●●○○○ 20 pts

Let a,a, b,b, cc be integers such that A=15(−3abc)\mathbf{A} = \frac{1}{5} \begin{pmatrix} -3 & a \\ b & c \end{pmatrix} and A2=I.\mathbf{A}^2 = \mathbf{I}. Find the largest possible value of a+b+c.a + b + c.

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matrix multiplicationinteger constraintsoptimization over integers