Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.1 Prove that $|GL_2(\mathbb{F}_2)| = 6$. Solution: $GL_2(\mathbb{F}_2$ consists of precisely those $2 \times 2$ matrices over…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.17 Let $n \in \mathbb{Z}^+$ and let $F$ be a field.Prove that the set $$UT_n^1(F) = \{…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.16 Let $n \in \mathbb{Z}^+$ and let $F$ be a field. Prove that the set $$UT_n(F) =…