Proving a Matrix is Invertible without Determinants – math.stackexchange.com

Proving a Matrix is Invertible without Determinants – math.stackexchange.com

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Prove if $A$, $B$, and $C$ are square matrices and $ABC = I$, then $B$ is invertible and ${B^{-1}}= CA$. I know that this proof can be done by taking the determinant of $ABC=I$ and showing that $A$, ...

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