Given A = [

2	−3
−4	7

]
|A| = 2 × - [(- 4) × (- 3)] = 2 ⇒ A−1 exist.
Cofactors of matrix A are
C11 = 7 , C12 = - 4 , C21 = - 3 , C22 = 2
Minors of matrix A are
M11 = (−1)1+1 × 7 = 7
M12 = (−1)1+2 × (- 4) = 4
M21 = (−1)3+1 × (- 3) = 3
M22 = (−1)2+2 × 2 = 2
A−1 =

1

2

(

7	3
4	2

)
2 A−1 = (

7	3
4	2

) ... (i)
9I - A = 9 (

1	0
0	1

)−(

2	−3
−4	7

)
= (

7	3
4	2

) ... (ii)
⇒ 2X−1 = 9I - A from (i) and (ii)