यदि `A={:[(1,2,3),(3,2,1),(2,3,1)]:}`, तो सिद्ध कीजिए कि `AI_(3)^(2)=I_(3)A`.

Explanation

`I_(3),3xx3` क्रम का आव्यूह है ।
`I_(3)={:[(1,0,0),(0,1,0),(0,0,1)]:}`
`I_(3)xxI_(3)=I_(3)^(2)={:[(1,0,0),(0,1,0),(0,0,1)][(1,0,0),(0,1,0),(0, 0, 1)]:}`
`={:[(1.1+0.0+0.0,1.0+0.1+0.0,1.0+0.0+0.1),(0.1+1.0+0.0,0.0+1.1+0.0,0.0+1.0+0.1),(0.1+0.0+1.0,0.0+0.1+1.0,0.0+0.0+1.1)]:}`
`={:[(1,0,0),(0,1,0),(0,0,1)]:}`
अब बाया पक्ष `AI_(3)^(2)={:[(1,2,3),(3,2,1),(2,3,1)][(1,0,0),(0,1,0),(0,0,1)]:}`
`={:[(1.1+2.0+3.0,1.0+2.1+3.0,1.0+2.0+3.1),(3.1+2.0+1.0,3.0+2.1+1.0,3.0+2.0+1.1),(2.1+3.0+1.0,2.0+3.1+1.0,2.0+3.0+1.1)]:}`
`={:[(1,2,3),(3,2,1),(2,3,1)]:}`
दाया पक्ष : `I_(3)A={:[(1,0,0),(0,1,0),(0,0,1)][(1,2,3),(3,2,1),(2,3,1)]:}`
`={:[(1,2,3),(3,2,1),(2,3,1)]:}`
अतः बाया पक्ष = दाया पक्ष