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**Maccaman** Determine if the given set (below) is a ring. If it is a ring, state if the ring is commutative, has identity, is an integral domain, and is a field.

(1)The set $\displaystyle S = \lbrace \ \begin{pmatrix} a&b\\b&a\end{pmatrix} \ | a,b,\in \ \mathbb{R} \rbrace $ under normal matrix addition and multiplication.

(2) The set of $\displaystyle \mathcal{F} $ of all functions $\displaystyle f: \mathbb{R} \ \rightarrow \ \mathbb{R} $ under pointwise addition (as the addition operation) and composition ( as the multiplication operation).

Thanks to anyone who can help