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If $A$ is any matrix, then the product $A A$ is defined only when $A$ is a matrix of order $m \times n$ where:
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The correct answer is:
$m=n$
A A is defined only when $A$ is a matrix of order $m \times n$ where $m=n$ $\mathrm{A} \times \mathrm{A}=(\mathrm{m} \times \mathrm{n})(\mathrm{m} \times \mathrm{n})=(\mathrm{m} \times \mathrm{n})(\mathrm{n} \times \mathrm{n})$ if $\mathrm{m}=\mathrm{n}$
$=\mathrm{m} \times \mathrm{n}=\mathrm{n} \times \mathrm{n}$ or $\mathrm{m} \times \mathrm{m}$
$=\mathrm{A}$ is a square matrix.
$=\mathrm{m} \times \mathrm{n}=\mathrm{n} \times \mathrm{n}$ or $\mathrm{m} \times \mathrm{m}$
$=\mathrm{A}$ is a square matrix.
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