® If AB = BA = I, where B is square matrix, then B is called inverse of A Also A–1 = B or B–1 = A and hence (A–1)–1 = A ® A square matrix A has inverse if and only if A is non-singular ®
–1
1
A
(
A adjA)
=
® If
a1 x + b1 y + c1 z = d1
a2 x + b2 y + c2 z = d2
a3 x + b3 y + c3 z = d3,
then these equations can be written as A X = B, where
1
1
1
1
2
2
2
2
3
3
3
3
A
,X=
and B=
a
b
c
x
d
a
b
c
y
d
a
b
c
z
d




 




 
=



 




 
 




® Unique solution of equation AX = B is given by X = A–1 B, where A
≠0