---
kind: statement
msc:
- 15A09
- 15B99
name: Invertibility of a triangular matrix
role: proposition
sources:
- locator: src/section3-1.xml:973
  url: https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section3-1.xml#L973
tag: 7X1B65CTG4
uses:
- GTG8MJGDKC
- 0EB9N0S33C
---

## Statement

Let $A$ be an $n \times n$ [[triangular matrix|GTG8MJGDKC]] over a field.
Then $A$ is an [[invertible matrix|0EB9N0S33C]] if and only if every entry on its main diagonal is nonzero.