= Inverse-matrix verification test
{title2=$AC=I$}
A claimed <inverse matrix> C for a finite square <matrix> A must satisfy $AC=CA=I$. A single product entry differing from the <identity matrix> disproves the claim. Conversely, in finite dimension one exact identity such as $AC=I$ already implies that A has full <rank>, so A is invertible and $C=A^{-1}$; the other product then equals I as well. Checking the product is useful before using a supplied inverse in a <similarity transformation>.
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