Matrix Entrywise Addition forms Abelian Group/Examples

Examples of Matrix Entrywise Addition forms Abelian Group

$2 \times 2$ Matrices over Rational Numbers

Let $\Q^{2 \times 2}$ denote the set of order $2$ square matrices over the set $\Q$ of rational numbers.

Then the algebraic structure $\struct {\Q^{2 \times 2}, +}$, where $+$ denotes matrix entrywise addition, is an abelian group.

$n \times n$ Matrices over Real Numbers

Let $\R^{n \times n}$ denote the set of order $n$ square matrices over the set $\R$ of real numbers.

Then the algebraic structure $\struct {\R^{n \times n}, +}$, where $+$ denotes matrix entrywise addition, is an abelian group.