Question

If a and b are square matrices of order n then prove that a and b will commute

Answer 1

H.S. = (A - B)(A + B) = A(A + B) - B(A + B)=(A−B)(A+B)=A(A+B)−B(A+B)

= A^2 + AB - BA - B^2=A

2

+AB−BA−B

2

This will become equal to L.H.S. only when AB = BAAB=BA