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

Question

Philoid · Accepted Answer

(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