यदि `A={:[(1,1,-1),(2,0,3),(3,-1,1)],B=[(1,3),(0,2),(-1,4)]" तथा "C=[(1,2,3,-4),(2,0,-2,1)]:}`, तो A (BC) तथा (AB) C ज्ञात कीजिए और दिखलाइए कि (AB) C=A (BC) है।

Explanation

`BC={:[(1,3),(0,2),(-1,4)][(1,2,3,-4),(2,0,-2,1)]:}`
`={:[(1+6,2+0,3-6,-4+3),(0+4,0+0,0-4,0+2),(-1+8,-2+0,-3-8,4+4)]=[(7,2,-3,-1),(4,0,-4,2),(7,-2,-11,8)]:}`
`A(BC)=[(1,1,-1),(2,0,3),(3,-1,2)][(7,-2,-3,-1),(4,0,-4,2),(7,-2,-11,8)]`
`={:[(7+4-7,2+0+2,-3-4+11,-1+2-8),(14+0+21,4+0-6+,-6+0-33,-2+0+24),(21-4+14,6+0-4,-9+4-22,-3-2+16)]`
`={:[(4,4,4,-7),(35,-2,-39,22),(31,2,-27,11)]:}`
अब `AB={:[(1,1,-1),(2,0,3),(3,-1,2)][(1,3),(0,2),(-1,4)]:}`
`={:[(1+0+1,3+2-4),(2+0-3,6+0+12),(3+0-2,9-2+8)]=[(2,1),(-1,18),(1,15)]:}`
`(AB)C={:[(2,1),(-1,18),(1,15)][(1,2,3,-4),(2,0,-2,1)]:}`
`={:[(2+2,4+0,6-2,-8+1),(-1+36,-2+0,-3-36,4+18),(1+31,2+0,3-30,-4+15)]:}`
`={:[(4,4,4,-7),(35,-2,-39,22),(31,2,-27,11)]:}`
अतः
(AB)C=A(BC).