IfA is an upper triangular n x n matrix, then det(A) is not equal to 0 . Why is this false?

Question

I am studying linear algebra and the book just confused me in a way I can't explain.

If A is an upper triangular n x n matrix, then det(A) is not equal to 0.

The book says this is false. Can someone explain why?

I understood that an upper triangular matrix gives a pivot to every column making every vector independent, thus the determinant can't be 0...

Answer 1

Consider the zero matrix. It is upper triangular, the determinant is zero.