1) Suppose that A is an nxn nonsingular upper triangualr matrix, and let B=A^-1. You may assume that all diagonal elements of A are nonzero.
a) using only the definition of matrix multiplication prove that Bsubnj =0 for all j<n. ( ie, show that all elements in the nth row of B, except for the last element, are zero.)
b) using only the definition of matrix multiplication , prove that B is upper triangular.