First slide

Operations of matrix

Question

If A and B are two matrices such that AB = B and BA = A, then A² + B² =

Moderate

A

2AB
B

2BA
C

A+B
D

AB

Solution

We have,
A²+ B²= AA + BB = A (BA) + B (AB)
( $∵$ AB = B and BA = A)
= (AB) A + (BA) B
= BA + AB = A + B
( $∵$ AB = B and BA = A)

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