यदि `A^(-1)=[(3,-1,1),(-15,6,-15),(5,-2,2)]`
और `B=[(1,2,-2),(-1,3,0),(0,-2,1)]` हो तो `(AB)^(-1)` का मान ज्ञात कीजिए ।

Explanation

`B=[(1,2,-2),(-1,3,0),(0,-2,1)]`
`:.|B|=|(1,2,-2),(-1,3,0),(0,-2,1)|`
`=1(3-0)-2(-1-0)-2(2-0)`
`=3+2-4=1!=0`
`B_(11)=3,B_(12)=1,B_(13)=2`
`B_(21)=2,B_(22)=1,B_(23)=2`
`=B_(31)=6,B_(32)=2,B_(33)=5`
`impliesadjB=[(3,1,2),(2,1,2),(6,2,5)]=[(3,2,6),(1,1,2),(2,2,5)]`
अब `B^(-1)=1/(|B|)adjB=[(3,2,6),(1,1,2),(2,2,6)]`
दिया है `A^(-1)=[(3,-1,1),(-15,6,-5),(5,-2,2)]`
`(AB)^(-1)=B^(-1)A^(-1)`
`=[(3,2,6),(1,1,2),(2,2,5)][(3,-1,1),(-15,6,-5),(5,-2,2)]`
`=[(9-30+30,-3+12-12,3-10+12),(3-15+10,-1+6-4,1-5+4),(6-30+25,-2+12-10,2-10+10)]`
`=[(9,-3,5),(-2,1,0),(1,0,2)]`