Question
If $A$ is a non$-$singular square matrix such that $|A| = 10,$ find $|A^{-1}|.$
✓
Answer
$\big|\text{A}^{-1}\big|=\Big|\frac{1}{\text{A}}\Big|$
$=\Big|\frac{1}{\text{A}}\Big|$
$=\frac{1}{10}\ \big[\because|\text{A}|=10\text{ (Given})\big]$
Hence, $\big|\text{A}^{-1}\big|=\frac{1}{10}$
$=\Big|\frac{1}{\text{A}}\Big|$
$=\frac{1}{10}\ \big[\because|\text{A}|=10\text{ (Given})\big]$
Hence, $\big|\text{A}^{-1}\big|=\frac{1}{10}$
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