Suppose that the matrix equation $AXB=C$ with unknown matrix $X$ is given, where $A$, $B$, and $C$\ are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation $AXB=C$ when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of symmetric and the set of skew-symmetric matrices are established as well. Moreover, some numerical examples are given for the problems considered.Comment: 10 page
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