First slide

Operations of matrix

Question

If A and B are two matrices such that AB = A and BA = B, then B² is equal to

Moderate

A

B
B

A
C

1
D

0

Solution

We have, AB= A and BA= B
$\begin{array}{ll} ∴ B^{2} = B B \\ \Rightarrow B^{2} = (B A) B [∵ B A = B] \\ \Rightarrow B^{2} = B (A B) \\ \Rightarrow B^{2} = B A [∵ A B = A] \\ \Rightarrow B^{2} = B [∵ B A = B] \end{array}$

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