%%visits: 2 Non-Scaling matrices, all square matrices with determinant 1. ## intuition ## rigour Z(SL(N, ℂ)) ≅ ℤn, as the centre must be a subset of Z(GL(N, ℂ)) ≅ ℂ×, now the determinant must be 1. So, $A = \lambda \mathbb{1}, \lambda \in \mathbb{C}^{\times} = det(A) = det(\lamda \mathbb{1}) = \lambda ^{n} = 1$ so it is the nth root of unity. We know that the roots of unity generate ℤn. If the centre can only be real, then lambda is 1 if n is odd, and lambda is in a group {1, −1} ≅ ℤ2 ## exam clinic ## examples and non-examples ## resources tags :math: