(a) Prove that the matrix RepK,B(id) changing bases in the direction opposite to that of the theorem has an upper triangular shape-all of its entries below the main diagonal are zeros.
(b) Prove that the inverse of an upper triangular matrix is also upper triangular (if the matrix is invertible, that is). This shows that the matrix RepB,K(id) changing bases in the direction described in the theorem is upper triangular.