Kunze Linear Algebra · Problem 5.3.7

Determinants

Mathematics — Methods · triangular-matrices-determinant

Problem

n \times n

matrix

A

is called triangular if

A_{ij} = 0

whenever

i > j

or if

A_{ij} = 0

whenever

i < j

. Prove that the determinant of a triangular matrix is the product

A_{11}A_{22} \cdots A_{nn}

of its diagonal entries.