First slide

Operations of matrix

Question

if A and B are two matrices such that AB = B and BA = A, then $A^{2} + B^{2}$ is equal to

Moderate

A

2AB
B

2BA
C

A+B
D

AB

Solution

Proceeding as in Example 2, we have
$A^{2} = A$ and $B^{2} = B$
$∴ A^{2} + B^{2} = A + B$

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