If \( \mathrm{M}=\left\{\left[\begin{array}{ll}x & x \\ x & x\end{array}\right], x \neq 0, x \in...

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If \( \mathrm{M}=\left\{\left[\begin{array}{ll}x & x \\ x & x\end{array}\right], x \neq 0, x \in \mathbf{R}\right\} \) and \( * \) be an operation on \( \mathrm{M} \) defined by \( \mathrm{A} * \mathrm{~B}=\mathrm{AB} \), for all \( A, B \in M \).
Prove that \( * \) is a binary operation on \( M \)
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