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Question

If A=111203312,B=130214 and C=[12342021], find A(BC),(AB)C and show that (AB)C=A(BC).

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Solution

Calculating: A(BC)
Given: A=111203312,B=130214 and C=[12342021]
BC=1302143×2 [12342021]2×4
BC=1+62+0364+30+40+0040+21+82+0384+4
BC=7231404272118
Now,
A(BC)=1112033123×3 72314042721123×4
A(BC)=444735239223122711 (1)

Calculating (AB)C
AB=1112033123×3 1302143 times2
AB=1+0+13+242+036+0+123+0292+8
AB=21118115
(AB)C=211181153×2 [12342021]2×4
=2+24+0628+11+362+03364+181+302+03304+15
(AB)C=444735239223122711 (2)
From equation (1) and (2)
(AB)C=A(BC)
Hence proved.

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