For [imath]i=2[/imath] you have [imath]M(M^{-1}K)^2=MM^{-1}KM^{-1}K=IKM^{-1}K=KM^{-1}K[/imath]

For [imath]i=3[/imath] you have [imath]M(M^{-1}K)^3=MM^{-1}KM^{-1}KM^{-1}K=IKM^{-1}KM^{-1}K=K(M^{-1}K)^2[/imath]

For [imath]i=4[/imath] you have [imath]M(M^{-1}K)^4=K(M^{-1}K)^3[/imath]

And for [imath]i=n[/imath] you have [imath]M(M^{-1}K)^n=K(M^{-1}K)^{n-1}[/imath]