Abstract Algebra: Theory and Applications · Problem 11.4.1

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · determinant-homomorphism

Problem

Prove that det⁡(AB)=det⁡(A)det⁡(B)\det(AB) = \det(A) \det(B) for A,B∈GL2(R)A, B \in GL_2(\mathbb{R}). This shows that the determinant is a homomorphism from GL2(R)GL_2(\mathbb{R}) to R∗\mathbb{R}^*.

Browse the problem library