# Matrix/n different eigenvalues/Determinant is product/Exercise

Let be a matrix with (pairwise) different eigenvalues. Show that the determinant of is the product of the eigenvalues.

Let ${}M\in \operatorname {Mat} _{n}(K)$ be a matrix with ${}n$ (pairwise) different eigenvalues. Show that the determinant of ${}M$ is the product of the eigenvalues.