16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.3.6

Determinants

Mathematics — Linear Algebra · determinant-identity-plus-a

Problem

Let AA be a 2×22 \times 2 matrix over a field. Prove that det⁡(I+A)=1+det⁡A\det(I + A) = 1 + \det A if and only if trace⁡(A)=0\operatorname{trace}(A) = 0.

Browse the problem library