What is the value of the determinant of the inverse of the matrix \begin{bmatrix}-4 & -5 \\ 2 & 2\end{bmatrix}?

Explanation

Let A = \begin{bmatrix}-4 & -5 \\ 2 & 2\end{bmatrix}. The determinant of A is |A| = (-4)(2) - (-5)(2) = -8 + 10 = 2. The determinant of the inverse matrix A^{-1} is \frac{1}{|A|} = \frac{1}{2}.

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