Question

Matrices A and B are inverse of each other only when 

A. AB = BA 

B. AB = BA = 0 

C. AB = 0, BA = I 

D. AB = BA = I

Answer 1

A = B^-1 

B = A^-1 

We know that 

AA^-1= I 

(Given B = A^-1) 

AB= I ------ 1 

We know that 

BB^-1= I 

(Given A=B^-1) 

BA= I ------ 2 

From 1 and 2 

AB = BA = I