If A and B are two matrices such that AB = B and BA = A, then A2 + B2 equals

Question

If A and B are two matrices such that AB = B and BA = A, then A2 + B2 equals (A) 2AB (B) 2BA (C) A + B (D) AB

Tardigrade Admin · Accepted Answer

Given, A B=B and B A=A Now, A2+B2 =A ⋅ A+B ⋅ B =A(B A)+B(A B)=(A B) A+(B A) B =B A+A B=A+B

Q. If $A$ and $B$ are two matrices such that $A B = B$ and $B A = A$ , then $A^{2} + B^{2}$ equals