If A[{:(3,-4),(1,1),(2,0):}] and B=[{:(2...

If `A[{:(3,-4),(1,1),(2,0):}]` and `B=[{:(2,1,2),(1,2,4):}]` , then verify AB = BA or not?

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We have, `A=[{:(2,1,2),(1,2,4):}]_(2xx3) "and" B=[{:(4,1),(2,3),(1,2):}]_(3xx2)`
So, AB and BA both are possible
[since, in both A-B and B-A, the number of columns of first is equal to the number of rows of second]
`therefore AB=[{:(2,1,2),(1,2,4):}]_(2xx3)[{:(4,1),(2,3),(1,2):}]_(3xx2)`
`=[{:(8+2+2,2+3+4),(4+4+4,1+ 6+8):}]=[{:(12,9),(12,15):}]`
and `BA=[{:(4,1),(2,3),(1,2):}]_(3xx2)[{:(2,1,2),(1,2,4):}]_(2xx3)`
`= [{:(4xx2+1,4+2,8+4),(4+3,2+ 6,4+12),(2+2,1+4,2+8):}]=[{:(9,6,12),(7,8,16),(4,5,10):}]`

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