# Matrix

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• Sep 8th 2009, 01:33 AM
roshanhero
Matrix
Explain why the notation A/B is ambiguous when A and B are matrices,even if det B isnot equal to 0.
• Sep 8th 2009, 01:48 AM
BobP
It's not ambiguous, the operation of dividing one matrix by another is not defined.
• Sep 8th 2009, 05:36 AM
HallsofIvy
I disagree with BobP. "Dividing", in any group, field, or ring, means multiplying by the inverse and is defined in a vector field.

The "ambiguity" is in A/B, and the reason "multiplying by the inverse" is never written that way, is that multiplication of matrices is not commutative. That could mean either $AB^{-1}$ or $B^{-1}A$.