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I know, I know. I should be awesome at these by now...

1. The problem statement, all variables and given/known data

Show if A,B,C are invertible matrices of the same size, than [itex](ABC)^{-1}=C^{-1}B^{-1}A^{-1}[/itex]

3. The attempt at a solutionGiven some matrix A,[itex]AA^{-1}=I[/itex]

If:

[itex]AA^{-1}=I[/itex]

[itex]BB^{-1}=I[/itex]

[itex]CC^{-1}=I[/itex]

I am not sure where to go from here. I don't think I have any more definitions or product rules to incorporate.

It almost seems as if I would FIRST have to show that (ABC) is invertible to begin with. Then I can use the fact that (ABC)(ABC)^{-1}=I to discover how (ABC)^{-1} MUST be arranged in order for the product of the two to yield I.

Does that sound like a good place to start? Proving if A,B, and C are invertible, then (ABC) is too?

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# Show if A,B,C are invertible matrices of same size...

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