Question

If $AB=A$ and $BA=B,$ then $A^2=$

• A. $A$
• B. $B$
• C. $A-B$
• D. $A+B$

Answer 1

The correct option is A $A$

$AB=A$

$\left(AB\right)A=AA$ [Multiplying both sides on right by $A$]

$A\left(BA\right)=A^2$ [By associative property}

$AB=A^2$ [$BA=B$]

$A=A^2$ [$AB=A$]

Thus, $A^2=A$.