If AB=A and BA = B then B^2 is equal to: 1. B 2. A 3. -B 4. B^2 - Vidyadip

Question

If $\text{AB}=\text{A}$ and $\text{BA = B}$ then $\text{B}^2 $ is equal to:

$\text{B}$
$\text{A}$
$\text{-B}$
$\text{B}^2$

✓

Answer

$\text{B}$

Solution:

We have, $\text{AB}=\text{A}$and $\text{BA = B}$

Since, $\text{B}^2=\text{B.B}$

$\text{B}^2=\text{(BA)}.\text{B}$

$\text{B}^2=\text{B}.\text{(AB)}$

$\text{B}^2=\text{B.A}$

$\text{B}^2=\text{B}$

Hence, this is the answer.

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