First slide

Operations of matrix

Question

{f $A$ and $B$ are two matrices such that $A B = A$ and $A = B,$ then $B^{2}$ is equal to

Moderate

A

$B$
B

$A$
C

1
D

0

Solution

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

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