Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication

We must show that the set satisfies the group requirements: Identity, Closure, Associativity and Invertibility.Identity: Contains identity matrixAssociativity: Follows from the rules of matrix multiplicationInvertibility: As none of the diagonal elements are non zero, if the reciprocal of each diagonal element is taken, the inverse can be obtainedClosure: Can show by example of multiplying two general matrices