Let \( A, B \) and \( C \) be \( 2 \times 2 \) matrices with entrie...

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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:
\[
A * B=\frac{1}{2}\left(A B^{\prime}+B A^{\prime}\right)
\]
(a) \( A * B=B * A \)
(b) \( A * A=A^{2} \)
(c) \( A *(B+C)=A * B+A * C \)
(d) \( 2 A * I=A+A^{\prime} \)
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