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If A and B are two non-singular square matrices such that $\mathrm{AB}=\mathrm{A}$, then which one of the following is correct?
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The correct answer is:
$\mathrm{B}$ is an identity matrix
Since, A and B are twonon-singular matrices therefore their determinant is non-zero. $\therefore \mathrm{A}^{-1}$ and $\mathrm{B}^{-1}$ defined.
Consider $\mathrm{AB}=\mathrm{A} \Rightarrow \mathrm{A}^{-1} \mathrm{AB}=\mathrm{A}^{-1} \mathrm{~A} \Rightarrow \mathrm{B}=\mathrm{I}$
Consider $\mathrm{AB}=\mathrm{A} \Rightarrow \mathrm{A}^{-1} \mathrm{AB}=\mathrm{A}^{-1} \mathrm{~A} \Rightarrow \mathrm{B}=\mathrm{I}$
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