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If A=[3sqrt(3)2 4 20]and B=[2-1 2 124], ...

If `A=[3sqrt(3)2 4 20]`and `B=[2-1 2 124]`, verify that(i) `(Aprime)prime=A` (ii) `(A+B)prime=Aprime+Bprime` (iii) `(k B)prime=k Bprime`where k is any constant.

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given matrix `A=[(3,sqrt(3),2),(4,2,0)]`and `B=[(2,-1,2),(1,2,4)]`
(i) `[[(3,sqrt(3),2),(4,2,0)]^']^'` = `[(3,4),(sqrt(3),2),(2,0)]^'` = `[(3,sqrt(3),2),(4,2,0)]`=A
(ii) `A+B = [(3,sqrt(3),2),(4,2,0)] + [(2,-1,2),(1,2,4)]` = `[(5,-1+sqrt(3),4),(5,4,4)]`
`(A+B)^' = [(5,5),(-1+(sqrt(3)),4),(4,4)]^'`
`A'=[(3,4),(sqrt(3),2),(2,0)]` & `B' = [(2,1),(-1,2),(2,4)] `
`A' +B' =[(3,4),(sqrt(3),2),(2,0)] + [(2,1),(-1,2),(2,4)] = [(5,5),(-1+sqrt(3),4),(4,4)]`
(iii) `KB= [(2k,-k,2k),(k,2k,4k)]`
`(KB)^' = [(2k,k),(-k,2k),(2k,4k)]`
`B^' = [(2,1),(-1,2),(2,4)] = kB^' = [(2k,k),(-k,2k),(2k,4k)]`
`(kB)^' = kB^'`
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