Let A be a lower triangular n × n matrix with nonzero entries on the diagonal. Show that...

Let A be a lower triangular n × n matrix with nonzero entries on the diagonal. Show that A is invertible and A^–1 is lower triangular. [Hint: Explain why A can be changed into I using only row replacements and scaling. (Where are the pivots?) Also, explain why the row operations that reduce A to I change I into a lower triangular matrix.]