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## Multiplication of 2×2 matrices over the real numbers is associative

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.9 Prove that the binary operation of matrix multiplication of $2 \times 2$ matrices over $\mathbb{R}$ is…

## Direct product of groups is essentially associative

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.12 Let $A$, $B$, and $C$ be groups. Show that \$A \times (B \times C) \cong (A…