Prove that if S: U-->V and T: V-->W are isomorphisms, then TS (composition) is also an isomorphism.(adsbygoogle = window.adsbygoogle || []).push({});

Idea: So my idea was since both S, T are both isomorphic that means they both have inverses S^{-1}and T^{-1}. Now this is where I'm a little grey, in order to show that TS is isomorphic, is it enough for me to obtain the identity transformation "I" by multiplying the composition TS through by S^{-1}T^{-1}, based on the properties of linearity?

TS = S^{-1}T^{-1}(TS) = S^{-1}S = I ? or would I have to show the existence of (TS)^{-1}? and if so how?

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# Homework Help: Showing a composition is isomorphic

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