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Question

If A=[1223], B=[2123] and C=[3120]. check whether
(AB)C=A(BC) and A(B+C)=BA+CA ?

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Solution

AB=[1223]×[2123]
=[1.2+2.21.1+2.3(2).2+3.2(2).1+3.3]
=[6727]
BC=[2123]×[3120]
=[6+22+06+62+0]
=[4202]
AC=[1223]×[3120]
=[3+41+06+62+0]
=[11122]
B+C=[2123]+[3120]
=[231+12+23+0]=[1243]
(i)(AB)C=[6727]×[3120]
=[18+146+06+142+0]=[4682]...(1)
A(BC)=[1223]×[4202]
=[4+02+48+04+6]=[4682]...(2)
From (1) and (2), we have (AB)C=A(BC)
(ii)A(B+C)=[1223]×[1243]
=[1+82+62+124+9]=[78145]...(3)
and AB+AC=[6727]+[11122]
=[6+17+12+1272]=[78145]...(4)
From (3) and (4), we have A(B+C)=AB+AC

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