Minimal polynomial of an invertible matrix
= Minimal polynomial of an invertible matrix
A square matrix $A$ is <invertible matrix>[invertible] exactly when its <minimal polynomial> has nonzero constant term. If $m_A(t)=tq(t)$, then $Aq(A)=0$, and invertibility would contradict the minimality of $m_A$. Conversely, if $m_A(t)=tq(t)+c$ with $c\ne0$, then $A[-q(A)/c]=I$.