यदि `A={:[(0,6,7),(-6,0,8),(7,-8,0)],B=[(0,1,1),(1,0,2),(1,2,0)],C=[(2),(-2),(3)]:}`, तो AC, BC तथा (A+B)C का परिकलन कीजिए । यह भी सत्यापित कीजिए कि (A+B)C=AC+BC.

Explanation

`AC={:[(0,6,7),(-6,0,8),(7,-8,0)],[(2),(-2),(3)]=[(0-12+21),(-12+0+24),(14+16+0)]=[(9),(12),(30)]:}`
`BC={:[(0,1,1),(1,0,2),(1,2,3)][(2),(-2),(3)]=[(0-2+3),(2+0+6),(2-4+0)]=[(1),(8),(-2)]:}`
`A+B={:[(0+0,6+1,7+1),(-6+1,0+0,8+2),(7+1,-8+2,0+0)]=[(0,7,8),(-5,0,10),(8,-6,0)]:}`
`(A+B)C={:[(0,7,8),(-5,0,10),(8,-6,0)][(2),(-2),(3)]=[(0,14,+24),(-10,+0,+30),(16,+12,+0)]=[(10),(20),(30)]:}`
अब `AC+BC={:[(9),(12),(30)]+[(1),(8),(-2)]=[(9+1),(12+8),(30-2)]=[(10),(20),(28)]:}`
अतः (A+B)C=AC+BC.