Discussion
A matrix has determinant 4. The determinant of its inverse is
Answer: D
Since \( AA^{-1} = I \) and the identity has determinant one:
\[ \det A \cdot \det(A^{-1}) = 1 \quad\Rightarrow\quad \det(A^{-1}) = \frac{1}{\det A} = \frac{1}{4} = 0.25 \]
It also shows at once that a singular matrix, having zero determinant, can have no inverse.
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