आव्यूह का परिवर्त और `[(a,b),(c,d)]` निकाले।

Explanation

मानाकि ` A = [(a,b),(c,d)] , "तो " A' [(a,c),(d,d)]`
अतः A का परिवर्त = `[(a,c),(b,d)]`
Second part : माना कि `A = [(a,b),(c,d)]= [(a_(11),a_(12)),(a_(21),a_(22))],`
जहाँ `a_(11) = a,a_(12) = b,a_(21) = b, a_(21) = c,a_(22) = d `
` A_(11) = a_(11` अर्थात , a का cofactor = `= (-1)^(1+1)।d। = d `
[Here |d| is a determinant of order one]
`A_(12) = a_(12)` अर्थात , b का cofactor `= (-1)^(1+2) |c| = (-1) = -c `
` A_(21) = a_(21)` अर्थात , c का cofactor `= (-1)^(2+1)|b| = - b `
` A_(22) = a_(22) ` अर्थात , d का cofactor ` = (-1)^(2+2)|a| = |a| = a `
माना कि `B= |(A_(11) , A_(12)),(A_(21),A_(22))|=|(d,-c),(-b,a)| therefore "adj" A = B'= |(d,b),(-c,a)|`