Question

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

A. AB^-1 

B.A^-1B 

C.A^-1B^-1 

D.B^-1A^-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