Question:
If $A$ is a non-singular square matrix such that $|A|=10$, find $\left|A^{-1}\right|$.
Solution:
For any non-singular matrix A,
$\left|A^{-1}\right|=\frac{1}{|A|}$
$\therefore\left|A^{-1}\right|=\frac{1}{10} \quad[\because|A|=10]$
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