First slide

Operations of matrix

Question

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

Moderate

A

A, B are idempotent
B

only A is idempotent
C

only B is idempotent
D

None of these

Solution

$AB = A, BA = B A^{2} = ABAB = A (BA) B = (AB) B = AB = A B^{2} = BABA = B (AB) A = (BA) A = BA = B$

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