Chapter 2, Problem 7CTA

For each statement that follows, answer true if the statement is always true and false otherwise. In the case of a false statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is no always true. Assume that all the given matrices are $n\times n$ .

A triangular matrix is nonsingular if and only if itsdiagonal entries are all nonzero.