निम्नलिखित में दिए गए प्रत्‍येक आव्यूहों के व्युत्‍क्रम (जिनका अस्तित्व हो) ज्ञात कीजिए।
`[(1,0,0),(0,cos alpha,sin alpha),(0, sin alpha,-cos alpha)]`

Explanation

माना `A=[(1,0,0),(0,cos alpha,sin alpha),(0,sin alpha,-cos alpha)]`
`implies|A|=+|(1,0,0),(0,cos alpha,sin alpha),(0, sin alpha, -cos alpha)|`
`=1(-cos^(2)alpha-sin^(2)alpha)-0+0=-1!=0`
`A_(11)=(-1)^(2)(-cos^(2)alpha-sin^(2)alpha)=-1`
`A_(12)=(-1)^(3)(0-0)=0`
`A_(13)=(-1)^(4)(0-0)=0`,
`A_(21)=(-1)^(3)(0-0)=0`
`A_(22)=(-1)^(4)(-cos alpha-0)=-cos alpha`
`A_(23)=(-1)^(5)(sin alpha-0)=-sin alpha`
`A_(31)=(-1)^(4)(0-0)=0`
`A_(32)=(-1)^(5)(sin alpha-0)=-sin alpha`
`A_(33)-(-1)^(6)(cos alpha -0)=cos alpha`
`:. adj A=[(-1,0,0),(0,-cos alpha, -sin alpha),(0,-sin alpha, cos alpha)]`
`=[(-1,0,0),(0,-cos alpha, -sin alpha),(0,-sin alpha,cos alpha)]`
अब `A^(-1)=1/(|A|)adjA=1/(-1)[(-1,0,0),(0,-cos alpha,-sin alpha),(0,-sin alpha, cos alpha)]`
`=[(1,0,0),(0, cos alpha, sin alpha),(0,sin alpha, -cos alpha)]`