Square Order 2 Matrices over Real Numbers form Ring with Unity

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Let $S$ denote the set of square matrices of order $2$ whose entries are the set of real numbers.

Then $S$ forms a ring with unity whose unity is the matrix $\begin {pmatrix} 1 & 0 \\ 0 & 1 \end {pmatrix}$.


This is an instance of Ring of Square Matrices over Field is Ring with Unity.