A matrix B is the multiplicative inverse
of the matrix A if
A B = I
and
B A = I
Notation:
The multiplicative inverse of A is denoted A
-1
For a real number
a
, if
b
satisfies
ab
= 1 =
ba
, then
b
=
=
a
-1
1
a
Sec 3.2
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A matrix B is the multiplicative inverse
of the matrix A if
A B = I
and
B A = I
Notation:
The multiplicative inverse of A is denoted A
-1
REMARKS:
1.
If there is an inverse, there is just one
2.
Only square matrices have inverses (why? check dimensions !)
3.
Not every square matrix has an inverse
For a real number
a
, if
b
satisfies
ab
= 1 =
ba
, then
b
=
=
a
-1
1
a
3.2.1
Saturday, February 06, 2010
11:16 PM
Section3dot2 Page 2