AB=[12−23]×[2123]
=[1.2+2.21.1+2.3(−2).2+3.2(−2).1+3.3]
=[6727]
BC=[2123]×[−3120]
=[−6+22+0−6+62+0]
=[−4202]
AC=[12−23]×[−3120]
=[−3+41+06+6−2+0]
=[1112−2]
B+C=[2123]+[−3120]
=[2−31+12+23+0]=[−1243]
(i)(AB)C=[6727]×[−3120]
=[−18+146+0−6+142+0]=[−4682]...(1)
A(BC)=[12−23]×[−4202]
=[−4+02+48+0−4+6]=[−4682]...(2)
From (1) and (2), we have (AB)C=A(BC)
(ii)A(B+C)=[12−23]×[−1243]
=[−1+82+62+12−4+9]=[78145]...(3)
and AB+AC=[6727]+[1112−2]
=[6+17+12+127−2]=[78145]...(4)
From (3) and (4), we have A(B+C)=AB+AC