A Matrix problem by hobart pao

Algebra Level 4

If \( A=\begin{pmatrix} 2 & 6 & 6 & 2 \\ 2 & 7 & 3 & 6 \\ 1 & 5 & 0 & 1 \\ 3 & 7 & 0 & 7 \end{pmatrix}\), what is the determinant of \(A^{-1}\)? Express the answer in the form \(-\dfrac{a}{b}\) in lowest terms, and find the sum \(a+b\).

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