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Let \( A, B \) and \( C \) be \( 2 \times 2 \) matrices with entries from the set of real numbers. Define \( * \) as follows:
\[
A * B=\frac{1}{2}(A B+B A) \text {, then }
\]
(a) \( A * B=B * A \)
(b) \( A * A=A^{2} \)
(c) \( A^{*}(B+C)=A^{*} B+A^{*} C \)
(d) \( A * I=A \)
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