Square Matrices over Real Numbers under Multiplication form Monoid
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Theorem
Let $\map {\MM_\R} n$ be a $n \times n$ matrix space over the set of real numbers $\R$.
Then the set of all $n \times n$ real matrices $\map {\MM_\R} n$ under matrix multiplication (conventional) forms a monoid.
Proof
$\blacksquare$
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 29$. Semigroups: definition and examples: $(4)$