If `A=[{:(5,4),(2,3):}]" and "B=[{:(3,5,1),(6,8,4):}]`, find AB and BA whichever exists.

If `A=[{:(5,4),(2,3):}]" and "B=[{:(3,5,1),(6,8,4):}]`, find AB and BA

1.	If `A=[{:(5,4),(2,3):}]" and "B=[{:(3,5,1),(6,8,4):}]`, find AB and BA whichever exists.
Answer» Here, A is a `2xx2` matrix and B is a `2xx3` matrix. Clearly, the number of column in A =number of rows in B. `:.` AB exists and it is a `2xx3` matrix. `AB=[{:(5,4),(2,3):}][{:(3,5,1),(6,8,4):}]` `=[{:(5.3+4.6,5.5+4.8,5.1+4.4),(2.3+3.6,2.5+3.8,2.1+3.4):}]` `=[{:(15+24,25+32,5+16),(6+18,10+24,2+12):}]=[{:(39,57,21),(24,34,14):}].` Again, B is a `2xx3` matrix and A is a `2xx2` matrix. `:.` number of columns in `Bne` number of rows in A. So, BA does not exist.

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If `A=[{:(5,4),(2,3):}]" and "B=[{:(3,5,1),(6,8,4):}]`, find AB and BA whichever exists.

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