Exercise 3.D.1

Answers

Proof. We have that

(T^{- 1} S^{- 1}) (ST) = T^{- 1} S^{- 1} ST = T^{- 1} T = I

And

(ST) (T^{- 1} S^{- 1}) = ST T^{- 1} S^{- 1} = S S^{- 1} = I

Hence $ST$ is invertible and ${(ST)}^{- 1} = T^{- 1} S^{- 1}$ . □

celiopassos

2017-10-06 00:00