If `A = [{:(0,1,2),(1,2,3),(2,3,4):}] and B=[{:(1,-2),(-1,0),(2,-1):}]` obtain the product AB and explain why BA is not defined?

Explanation

Here, the number of columns in A=3= the number of rows in B. therefore , the product AB is defined.
`AB[(0,1,2),(1,2,3),(2,3,4)][(R_(1),""),(R_(2),xx),(R_(3),"")]overset(C_1" " C_2)([(1,-2),(-1,0),(2,-1)]`

for convenience of multiplication we write colums in horizontal rectangle.

`=[{:(0xx1+1xx(-1)+2xx2,0xx(-2)+1xx0+2xx(-1)),(1xx1+2xx(-1)+3xx2,xx(-2)+2xx0+xx(-1)),(2xx1+3xx(-1)+4xx2,2xx(-2)+3xx0+4xx(-1)):}]_(3xx2`
`=[(0-1+4,0+0-2),(1-2+6,-2+0-3),(2-3+8,-4+0-4)]_(3xx2)`
`=[(3,-2),(5,-5),(7,-8)]_(3xx2)`
Since, the number of columns of B is 2 and the number of rows of A is 3, BA is not defined `(therefore2!=3).`