Question

If A and B are invertible matrices of the same order, then prove that (AB)^-1 = B^-1 A^-1.

Answer 1

From definition of inverse of matrix (AB) 

(AB)^-1 = 1 

A^-1 (AB)(AB)^-1 = A^-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 

l(AB)^-1 = B^-1 A^-1 

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