If AB = A and BA = B, then - Vidyadip

MCQ

If $AB = A$ and $BA = B$, then

A
$A^2B = A^2$
B
$B^2A = B^2$
C
$ABA = A$
✓
All of the above

✓

Answer

Correct option: D.

All of the above

d
We have $A^2B = A(AB) = AA = A^2$, $B^2A = B(BA) = BB = B^2$,
$ ABA = A(BA) = AB = A$, and $BAB = B(AB) = BA = B$

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