First off, I'm trying to prove that $(A^{-1})^{-1} = A$, but in my proof, I assume that $A^{-1}$ is invertible. I'd like to see or do a proof that $A^{-1}$ must be non-singular, but I'm stuck at square one.
2026-03-29 05:50:07.1774763407
How to prove that a matrix inverse is invertible?
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By definition a matrix A is the inverse of another matrix B if $AB = BA = Id$. It is clear from the equation above that if $A$ is the inverse of $B$ then $B$ is the inverse of $A$.