Show that if a triangular square matrix is nonsingular its d

Show that if a triangular square matrix is nonsingular, its diagonal entries are all nonzero.

Solution

We know that the determinant of a triangular square matrix is equal to the product of entries on the diagonal. Hence, a product of factors is nonzero iff every factor is nonzero.

thus, if a triangular square matrix is nonsingular, its diagonal entries are all nonzero.