I am reading a proof of the Cayley-Hamilton theorem which uses the fact that $adj(A)A=det(A)I$, where I is the $n\times n$ identity matrix and $A\in M_n(\mathbb{F})$ for a field $\mathbb{F}$.
Could you indicate me a quick way of proving this or to a reference proving it ?
And is is true for a matrix with coefficients over any commutative ring ? I would guess so because C-H is true for any commutative ring. In this case, is the proof the same ?
Thanks
