Why are operators often written in 3s?

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In a lot of my quantum mechanics and linear algebra books, operators are often defined as $M=IMI$ and many operations on operators are often done in similar fashion, for eg. operator $M$ might be sandwhiched between $H$ and $H^+$ (hermitian conjugate of H). What does $M=IMI$ mean and why is it written like that? Here is another example.