Division (mathematics)
Left and right division

Because matrix multiplication is not commutative, one can also define a left division or so-called backslash-division as A \ B = A B. For this to be well defined, B need not exist, however A does need to exist. To avoid confusion, division as defined by A / B = AB is sometimes called right division or slash-division in this context.

With left and right division defined this way, A / (BC) is in general not the same as (A / B) / C, nor is (AB) \ C the same as A \ (B \ C). However, it holds that A / (BC) = (A / C) / B and (AB) \ C = B \ (A \ C).
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