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For each of the following, write Y if the given “operation” is a well-defined binary operation on the given set; otherwise, write N. In each case in which it *isn't* a well-defined binary operation on the set, provide a *brief* explanation. You do not need to prove or explain anything in the cases in which it *is* a binary operation.

\(+\) on \(\C^*\)

\(*\) on \(\R^+\) defined by \(x*y=\log_x y\)

\(*\) on \(\M_2(\R)\) defined by \(A*B=AB^{-1}\)

\(*\) on \(\Q^*\) defined by \(z*w=z/w\)