Diketahui matriks A = (-2 1 3 3 2 5 2 1 -2), tentukan

Adj(A) = [[-9, 5, -1], [16, -2, 19], [-1, 4, -7]]

Pembahasan

Untuk mencari adjoin (adj(A)) dari matriks A, kita perlu menghitung matriks kofaktornya terlebih dahulu, lalu mentranspose matriks kofaktor tersebut. 

Matriks A = 
[ -2  1  3 ]
[  3  2  5 ]
[  2  1 -2 ]

Menghitung minor untuk setiap elemen:
Minor A11 = (2*-2) - (5*1) = -4 - 5 = -9
Minor A12 = (3*-2) - (5*2) = -6 - 10 = -16
Minor A13 = (3*1) - (2*2) = 3 - 4 = -1
Minor A21 = (1*-2) - (3*1) = -2 - 3 = -5
Minor A22 = (-2*-2) - (3*2) = 4 - 6 = -2
Minor A23 = (-2*1) - (1*2) = -2 - 2 = -4
Minor A31 = (1*5) - (3*2) = 5 - 6 = -1
Minor A32 = (-2*5) - (3*3) = -10 - 9 = -19
Minor A33 = (-2*2) - (1*3) = -4 - 3 = -7

Matriks Minor M = 
[ -9 -16  -1 ]
[ -5  -2  -4 ]
[ -1 -19  -7 ]

Menghitung kofaktor dengan aturan tanda (+ - + / - + - / + - +):
Kofaktor C = 
[ -9  16  -1 ]
[  5  -2   4 ]
[ -1  19  -7 ]

Adjoin(A) adalah transpose dari matriks kofaktor:
Adj(A) = Cᵀ = 
[ -9   5  -1 ]
[ 16  -2  19 ]
[ -1   4  -7 ]