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I am trying to use Maxima to simplify a symbolic matrix expression. I've learned that there are the non-commutative multiplication . and the non-commutative power ^^ operators. So I can write something like the following:

e1: X^^(-1) . (X^^(-1) + Y^^(-1))^^(-1) . Y^^(-1);

How could I force Maxima to apply the rule of the inverse matrix product here?

A^^(-1) . B^^(-1). C^^(-1) is (C.B.A)^^(-1), and then the initial expression is simplified to (X+Y)^^(-1).

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