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

MCQ

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

A
$B=I$
B
$A=I$
✓
$A^2=A$
D
$B^2=I$

✓

Answer

Correct option: C.

$A^2=A$

$A=A B=A(B A)=(A B) A=A \cdot A=A^2$
$B=B A=B(A B)=(B A) B=B \cdot B=B^2$

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