Cayley–Hamilton theorem: every square matrix satisfies its characteristic polynomial, $p_A(A)=0$. One proof expands the polynomial identity $(tI-A)\operatorname{adj}(tI-A)=p_A(t)I$, compares coefficients, and combines the resulting matrix recurrences. Avoid treating $t=A$ as an automatic scalar substitution into a determinant; the theorem is the justification.
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.