Cayley's matrix memoir

Arthur Cayley's 1858 paper A Memoir on the Theory of Matrices motivates matrices as an abbreviated way to write systems of linear equations. Its opening already connects the characteristic equation with reducing polynomials in a matrix to lower degree. In §21 he works out the two-by-two identity; in §23 he says he has verified the three-by-three case but does not give a formal proof for every size. Thus this source distinguishes the general statement from a general proof.^[ref] The theorem's name also commemorates William Rowan Hamilton.