Let's do another one:

A = [ row 1: 3 , -5  row 2: 2 , 8 ]

B = [ row 1: 6 , 0 , -4 , -2  row 2: -9 , 8 , 7 , 5 ]

Can we do  B times A ?

B times A ... 2 x 4 times 2 x 2 ... No! ... the 4 and the 2 don't match

What about  A times B ?

A times B ... 2 x 2 times 2 x 4 ... Yep! ... the 2's match

Let's go!

A = [ row 1: 6 , 0 , -4 , -2  row 2: -9 , 8 , 7 , 5 ] ... B = [ row 1: 3 , -5  row 2: 2 , 8 ] ... C ( the answer matrix ) = [ row 1: 63 , -40 , -47 , -31  row 2: -60 , -64 , 48 , 36 ]

Check my work!  Did I get them all right?  I was pretty sleepy when I did this and I was watching a really good Seinfeld.

Do you see how I got everything?