Question

If A and B are invertible matrices of the same order then (AB)^-1 = ? 

A. (A^-1 х B^-1) 

B. (A х B^-1) 

C. (A^-1 х B) 

D. (B^-1 х A^-1)

Answer 1

(AB)(AB)^-1 = I 

A^-1(AB)(AB)^-1 = IA^-1 

(A ^-1A)B (AB) ^-1=A^-1 

IB(AB)^-1 = A^-1 

B(AB)^-1 = A^-1 

B^-1B(AB)^-1 = B^-1 A^-1 

I (AB)^-1 = B^-1A^-1 

(AB)^-1 = B^-1A^-1