Question

If A and B are two matrices such that AB = B and BA = A, then A² + B² is equal to :

A. 2AB 

B. 2BA 

C. A + B 

D. AB

Answer 1

(C). A + B 

AB = A ----- (i) 

BA = B ------(ii) 

From equation (ii),

B × (AB) = B 

B²A= B 

From equation (ii), 

B²A = BA 

B² = B

From equation (i),

A × (BA) = A 

A²B = A 

From equation (i),

A²B = AB 

A² = A 

Hence, 

A² + B² = A + B. 

Option (C) is the correct answer.