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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?