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If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):...

If `A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]` a=4 and b=-2, then show that
(i) A+(B+C)=(A+B)+C
(b) A(BC)=(AB)C
(iii) (a+b)B=aB+bB
(iv) a(C-A)=aC-aA
(v) `(A^(T))^(T)=A`
(vi) `(bA)^(T)=bA^(T)`
(vii) `(AB)^(T)=B^(T)A^(T)`
(viii) `(A-B)C=AC-BC`
(ix) `(A-B)^(T)=A^(T)-B^(T)`

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