Aspire Faculty ID #18358 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

If $A$ and $B$ are two square matrices such that $AB = A$ and $BA = B$, then

Solution

Given $AB = A$ Multiply by $A$: $A(AB) = A^2 \Rightarrow A^2 = A$ Similarly, from $BA = B$: $B^2 = B$ Hence both are idempotent Final Answer: $\boxed{\text{A and B are idempotent}}$
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