Question

If A and B are square matrices of same order such that AB = BA, then $A^2 + B^2$ is equal to :

• A. $A + B$
• B. $BA$
• C. $2(A + B)$
• D. $2BA$

Hint:

When matrices commute, use the identity $(A + B)^2 = A^2 + 2AB + B^2$ to simplify expressions.

Answer 1

The Correct Option is C

Given that $AB = BA$, we can use this property to simplify the expression for $A^2 + B^2$. \[ A^2 + B^2 = (A + B)^2 - 2AB \] Since $AB = BA$, we have: \[ A^2 + B^2 = (A + B)^2 - 2AB = 2(A + B) \] Thus, the correct answer is $2(A + B)$.