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Exercise 3.D.11

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Proof. By Exercise 9 and Exercise 10 it follows that $S$ , $T$ and $U$ are all invertible. Multiplying both sides of $STU = I$ from the left by $S^{- 1}$ and then from the right by $U^{- 1}$ we get $T = S^{- 1} U^{- 1} = {(US)}^{- 1}$ , which implies $T^{- 1} = US$ . □

celiopassos

2017-10-06 00:00

Exercise 3.D.11

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