Prove that the monoid $M_n(\mathbb{R})$, where the operation is matrix multiplication, is isomorphic to $M_n(\mathbb{R})^{op}$ I just need a hint as to what to pick for a function. I know that I have to prove the there exists a bijective mapping that preserves the operations and maps the identity from $M_n(\mathbb{R})$ to the identity in $M_n(\mathbb{R})^{op}$. I am just having difficulty in choosing a mapping.

Take$$\begin{array}{ccc}M_n(\mathbb{R})&\longrightarrow&M_n(\mathbb{R})\\M&\mapsto&M^t.\end{array}$$
