First slide

Operations of matrix

Question

If AB = A and BA = B, then B² is equal to

Moderate

A

B
B

A
C

1
D

0

Solution

Since BA = B
$∴ (B A) B = B B = B^{2}$
$\Rightarrow B (A B) = B^{2} \Rightarrow B A = B^{2} (∵ A B = A)$
$\Rightarrow B = B^{2} (∵ B A = B)$

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