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For the matrices A and B, verify that (A...

For the matrices A and B, verify that `(A B)^(prime)=B^(prime)A^(prime)`, where(i) `A=[1-4 3]`,`B=[-1 2 1]` (iii) `A=[0 1 2]`,`B=[1 5 7]`

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The correct Answer is:
N/a
`(i) A=[{:(-1),(4),(3):}] implies A'=[-1" " 4 " "3]`
`b=[-1" " 2" " 1]implies B]=[{:(-1),(2),(1):}]`
`therefore AB=[{:(-1),(4),(3):}][-1" " 2" " 1]=[{:(1,-2,-1),(-4,8,4),(-3,6,3):}]`
`implies (AB')'=[{:(1,-4,-3),(-2,8,6),(-1,4,3):}]`
`and B'A =[{:(-1),(2),(1):}][-1" " 4" "3]=[{:(1,-4,-3),(-2,8,6),(-1,4,3):}]`
`therefore (AB)'=B'A'` hence proved
`(ii) A=[{:(0),(1),(2):}]implies A'[0" " 1" " 2]`
`B=[1" "5" "7]=[{:(0,0,0),(1,5,7),(2,10,14):}]`
`implies (AB)'=[{:(0,1,2),(0,5,10),(0,7,14):}]`
`implies B'A'=[{:(1),(5),(7):}][0" " 1" " 2]=[{:(0,1,2),(0,5,10),(0,7,14):}]`
`therefore (AB')' =B'A'` hence proved .
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