Question

Let A, B be two square matrices such that A + B = AB, then

(A) AB = BA 

(B) AB = -BA 

(C) AB + 2BA = 0 

(D) None of these

Answer 1

Answer is (A)

A + B = AB A + B – AB = 0 

A + B – AB + I = 0+1 

(A – I)(B – I) = 1 

⇒ A -1 inverse of B -1 

(B -1) (A -1) = I 

BA – B – A + = I 

BA – (B + A) 

⇒ BA = B + A 

= A + B 

∴ AB = BA