We can assume that the matrix A is upper triangular and invertible, since

We can prove that is upper triangular by showing that

the adjoint is upper triangular or that the matrix of cofactors is lower

triangular. Do this by showing every cofactor with

i<j(above the diagonal) is 0.

Since it suffices to show that

each minor with i<j is 0.

Start by letting be the matrix we get when the ith row

and jth column of A are gotten rid of (deleted).

Can you go further?.

There is a handy theorem which we won't prove, but use, which says:

"If A is an nXn triangular matrix then det(A) is the product of the entries on the main diagonal of the matrix. What I mean is