If A and B are two matrices such that

Question:

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

(a) $B$

(b) $A$

(c) 1

(d) 0

Solution:

(a) $B$

Here,

$A B=A \quad \ldots(1)$

$B A=B \quad \ldots(2)$

$\Rightarrow B A B=B B \quad[$ Multiplying both sides by $B]$

$\Rightarrow B A=B^{2} \quad$ [From eq. (1)]

$\Rightarrow B=B^{2} \quad$ [From eq. (2)]

 

 

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