The determinant of a triangular matrix is the product of the entries on the diagonal.

Theorem: The determinant of a triangular matrix is the product of the entries on the diagonal: $\det(T) = t_{11} \cdot t_{22} \cdots t_{nn}$. This follows from cofactor expansion or from the fact that the eigenvalues of a triangular matrix are its diagonal entries and $\det(A) = \prod \lambda_i$.