Ah, I understand. Is there some more in-depth documentation for the online Wolfram|Alpha, besides the examples? I ran into similar problems before, but I always only find the Wolfram Language reference and the Wolfram|Alpha API documentation, and would be happy to understand such problems myself!

Oh, that explains my stumpedness, thanks Robert!

Then I'm only a bit confused why the asterisk is interpreted as a dot in the second case, since the result there is a real matrix product - that is what lead me to believe the asterisk does what I want in the first place :D Using the query ((1,2,3),(-1,0,1),(2,1,1)) * ((3,-2,0),(1,-1,0),(-7,4,1)), the visual representation of Wolfram|Alpha also shows the asterisk as a dot, while with inverse (((1,2,3),(-1,0,1),(2,1,1)) * (inverse ((1,-2,0),(1,-3,0),(3,-2,1)))), no operator is shown between the matrices.

In any case, I now know how to tell Wolfram|Alpha what I want it to do!

Oh sorry, I only put the queries as description of the corresponding pictures.

Actually, I just found the source of the weirdness: The first query is

inverse (((1,2,3),(-1,0,1),(2,1,1)) * (inverse ((1,-2,0),(1,-3,0),(3,-2,1))))

the successful one ist

inverse (((1,2,3),(-1,0,1),(2,1,1)) * ((3,-2,0),(1,-1,0),(-7,4,1)))

If I instead of the " * " use " . ", the first query is working as expected as well. Looking at the examples now, the dot is used for matrix products, but for some instances the asterisk yields the same result as the dot, which lead me to believe they're interchangeable.

I didn't find an example of what the asterisk should actually do, so is it expected that it does something different when used in the first query?