An algebra problem by أحمد الحلاق

Algebra Level 4

Let \( A = \begin{bmatrix}{3} & {2} \\ {2} & {2}\end{bmatrix} \). Evaluate \[ \det (4(A^{-1})) + \det (4(A^{-1})^2) + \det (4(A^{-1})^3) + \cdots + \det (4(A^{-1})^6) \]

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