To travel regularly over some distance, as from a suburb into a city and back. She commutes to the city every day for work.
To change a penalty to a less severe one. The governor decided to commute his death sentence to life imprisonment.
To exchange one kind of payment or obligation for another. He decided to commute his pension into a lump sum payment.
To have a commutative relationship; to yield the same result when the order of two operations or elements is reversed. In linear algebra, matrices A and B commute if AB equals BA.