18.4 The inverse matrix 515
2.Transpose the matrix of cofactors:
The matrix™is called the adjointofA.
3.Divide the adjoint matrix by the determinant of A:
(18.45)
EXAMPLE 18.16The inverse of order 2
The matrix
has determinant det 1 A 1 = 1 a
11a
221 − 1 a
12a
21, and the cofactors of its elements areC
111 = 1 a
22,
C
121 = 1 −a
21,C
211 = 1 −a
12,C
221 = 1 a
11. Then
so that
This is the same as formula (18.43).
0 Exercise 47
EXAMPLE 18.17Find the inverse of
A=−
−
213
420
110
.
A
−=
−
−
−
111 22 12 2122
1221 111
aa aa
aa
aa
™==
−
−
CC
CC
aa
aa
11
2112 2222
1221 11A=
aa
aa
11
1221 22A
A
−=
1™
det
→
CC C
CC C
CC C
nnn
nnn11 21 112 2221
2
=Â