I thought matrix multiplication wasn't commutative, and that the number of columns in the multiplier must be equal to the number of rows in the multiplicand. Is this a glitch? Also, could anyone explain to me the matrix plot Wolfram Alpha displays for matrices?

Enter this into Wolfram Alpha to see for yourself.
{{4,3},{2,5},{6,8}}{3,1,4}

Here's a direct link.

https://www.wolframalpha.com/input/?i=%7B%7B4%2C3%7D%2C%7B2%2C5%7D%2C%7B6%2C8%7D%7D%7B3%2C1%2C4%7D