A triangular matrix is nonsingular if and only if its diagonal entries are all nonzero. In the

Question:

A triangular matrix is nonsingular if and only if its diagonal entries are all nonzero.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true. In each of the following, assume that all the matrices are n × n.