MathCastle
Groups and FieldsChallengeGroup Actions

Group Actions · Challenge problem

GL(2,Z2)GL(2,\mathbb Z_2) acts on the 1616 2×22\times2 matrices over Z2\mathbb Z_2 by conjugation: g⋅X=gXg−1g\cdot X=gXg^{-1}. How many orbits are there?