Let \(k\) be a field and let \(A\in\Mat_{n\times n}(k)\) be upper triangular with every diagonal entry equal to \(1\). Then \(A - I\) is strictly upper triangular, so \((A-I)^n = 0\) and \(A\) is unipotent.
Unipotent element
D-23FX7
D-23FX7
Let \(k\) be a field and let \(A\in\Mat_{n\times n}(k)\) be upper triangular with every diagonal entry equal to \(1\). Then \(A - I\) is strictly upper triangular, so \((A-I)^n = 0\) and \(A\) is unipotent.