Matrix Determinant Adjoint Power (Jee Mains)

Determinants

Medium

Matrix Determinant Adjoint Power

Let A = $\left[ {\begin{array}{*{20}{c}} 2&{2 + p}&{2 + p + q}\\[0.9em] 4&{6 + 2p}&{8 + 3p + 2q}\\[0.9em] 6&{12 + 3p}&{20 + 6p + 3q} \end{array}} \right]$ .
If det (adj (adj(3A))) = 2^m · 3ⁿ, m, n ∈

, then m + n is equal to

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