1) The cofactor of an element in a matrix is obtained by deleting the row and column of that element and calculating the determinant of the resulting (m-1)x(m-1) submatrix. 2) The cofactor matrix of a matrix A is denoted by adj(A) and its elements are given by (-1)i+j times the cofactor of the element in the ith row and jth column of A. 3) For a square matrix A of order n, the adjoint of A is equal to the transpose of the cofactor matrix, or adj(A)=[AT] where AT is the transpose of A.

1. lCnoy dmol CoAadoy o{ a vlalAn
Vlino e am Elned:
Ler t-aimim a ane
mmalux, Them M: dimate a suh-mnalux of d
mg
w on de (m-1) x(m-1) 0blaumed by deleti
aw
l h Aaw and jh column, lhedeleammima
I l callecl the nimoi o Whe elemeut
Cotale o am Elemenl:
he co{acla o m elntur
a den@teddoyA amd meol a
(-1 Ml
onnol cejaclous matin LAjaxm
Mdjoi a ALLane mmatun ot Cud
3:
The hompan CokQdas malux
non called Dnadjo o
amd u deneteel Jay adj ()
adyA)=[ AT

2. wnveu a A-quann matun ot@rde n23:
Cet be
d m.
hem the mmultiplicauue imVuse
anoy mmgulau mmalux (ie |Alt0
uolmeleod by amd ib dekimeek
aol CAJ
AI
f3
EOnpler Let 3
o
33
Find () Coraoln matu n e A
w hdljCA)
(Lut 7
A
olulim
0) we Rnow Cafalan o om elemenl
Qio A given b
O
Ihu tte catalan mmatuA a
i ve
mai a t ll be

3. A
33 S 3
Now himolimg all Aj by wmma )
3
2
=(-1)|3-2
o
(-3-- 13 6
2 0
2 o
Ct3- 2 -C
9C-D2" |M,
)3 3 2 2
-4 0
C- 3 2,
3

4. =()3 2
3-
2
-1) 3 2
3
t-
a-GH*|JM,
-1) 3 2 -
3
A33(-1)373 2
3
2
Hence he Cojod malux o
Tt 13 6-I
42 1C
l lo I
aalj CA)= "lAJ]
-IL
1
ad (A)=
-lo 1

5. 7
9

6. N
N

7. 1Al= 2 3
3 2 242 3
Jimu IAI+0, 9o eudhomdtü
in
Cam Jae w.llem aas
XAB
Now uue himol aolj (A) th cetoelo
2 10
3H3
Cveuy youuselj)
A 4An 2 A3lo A2,4,A-1
A30 Asg
uhene
A23C H3=1
Now,
adjtA)=Lh;
aoly(A)=-
t0
amo AadjA) =
)
18
L

8. T