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.