I just realized WolframAlpha arbitrarily decides which way to multiply matrices based on seemingly irrelevant stuff, and I'd like to understand whether the issue is with my knowledge of what's expected or whether it's Wolfram being a weirdo.
I'll explain further:
- If I enter two matrices side by side, Wolfram performs a dot product (which is what I'd expect).
- If I raise a matrix to the -1, Wolfram does its inverse properly.
- If I enter two matrices side by side, and raise any of them to the -1, it suddenly decides that the product should be element-wise instead of a dot product (it even does it "wrong" when the two matrices are different sizes).
- If I place a dot between them, then it does the dot product I was expecting.
Is this the default behavior we should expect or it's just a huge bug they have?
PS: Replicating this is as easy as calculating $I^2A$ with the math input mode matrices (writing the $I$ by hand, and chosing any $A$ you may like).