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Let $\mathrm{A}$ be an $\mathrm{m} \times \mathrm{n}$ matrix. Under which one of the following conditions does $\mathrm{A}^{-1}$ exist?
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Verified Answer
The correct answer is:
$\mathrm{m}=\mathrm{n}$ and $\operatorname{det} \mathrm{A} \neq 0$
Let a be an $\mathrm{m} \times \mathrm{n}$ matrix, then $\mathrm{A}^{-1}$ will exist if $\mathrm{m}=\mathrm{n}$ since only square matrix has determinant and det A $\neq 0$
$\left[\right.$ Since $\left.A^{-1}=\frac{\text { adjA }}{|A|}\right]$
$\left[\right.$ Since $\left.A^{-1}=\frac{\text { adjA }}{|A|}\right]$
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