SOLUTION: Find if they exist (a) AB (b) BA and (c) A^2 when A=[3 2 1] and B =[2 3 0]

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Question 1034918: Find if they exist (a) AB (b) BA and (c) A^2 when
A=[3 2 1] and B =[2
3
0]
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A%22%22=%22%22%28matrix%281%2C3%2C3%2C2%2C1%29%29 and B%22%22=%22%22%28matrix%283%2C1%2C2%2C3%2C0%29%29

A is a 1 'down' by 3 'across' matrix.
B is a 3 'down' by 1 'across' matrix.

The only time two matrices can be multiplied are when
the 'across' number of the left matrix equals the 'down' 
number of the matrix on the right. 

Then the product matrix has the 'down' number of the
left matrix and the 'across' number of the right matrix.

So the product matrix AB will be a 1 'down' by 1 'across':

So only AB is possible:

AB%22%22=%22%22%28matrix%281%2C3%2C3%2C2%2C1%29%29%28matrix%283%2C1%2C2%2C3%2C0%29%29%22%22=%22%22%28matrix%281%2C1%2C3%2A2%2B2%2A3%2B1%2A0%29%29%22%22=%22%22%28matrix%281%2C1%2C6%2B6%2B0%29%29%22%22=%22%22%2812%29

Neither BA nor A2 exist.

Edwin