Prove that determinant of triangular matrix is the product of its diagonal ennltries.

Question

Prove that determinant of triangular matrix is the product of its diagonal entries.

I want to use $\operatorname{'sgn'}$.I know that $\operatorname{det}(A)=\sum\limits_{\sigma}A(1,\sigma1)...A(n,\sigma n)$.Any help.

Thanks in advance.