We performed AB above, and the answer was:

`{:(AB, = ((0,-1,2),(4,11,2)) ((3,-1),(1,2),(6,1)) ),(, = ( (11,0),(35,20) )) :}`

Now BA is (3 × 2)(2 × 3) which will give 3 × 3:

`{: (BA,= ((3,-1),(1,2),(6,1))((0,-1,2),(4,11,2)) ), (, = ((0-4,-3-11,6-2),(0+8,-1+22,2+4),(0+4,-6+11,12+2)) ), (,= ((-4,-14,4),(8,21,6),(4,5,14)) ) :}`

So in this case, AB does NOT equal BA.

In fact, for most matrices, you cannot reverse the order of multiplication and get the same result.