Complex sentence: When matrices or members of various other associative algebras are multiplied the product usually depends on the order of the factors; in other words, matrix multiplication, and the multiplications in those other algebras, are non-commutative.
Split into simpler sentences: When matrices or members of various other associative algebras are multiplied, the product usually depends on the order of the factors. Matrix multiplication, and the multiplications in the other algebras, are non-commutative.