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Properties of inverses of matrices - class-XII
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Matrices $A$ and $B$ will be inverse of each other only if
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A
$AB=BA=I$
💡 Explanation:
We know that if $A$ is a square of order $m$, and if there exists another
square matrix $B$ of the same order $m$, such that $AB=I$, then $B$ is said
to be the inverse of $A$.
In this case, it is clear that $A$ is the inverse
of $B$.
Thus , matrices $A$ and $B$ will be inverses of each other only if $AB=BA=I.$
of $B$.
Thus , matrices $A$ and $B$ will be inverses of each other only if $AB=BA=I.$