The multiplicative inverse of a real number is the number that yields 1 (the identity) when multiplied by the original number. is the multiplicative inverse of a , because a× = 1 .
Most matrices also have a multiplicative inverse. In other words, for
the majority of matrices
A
, there exists a matrix
A
^{-1}
such that
AA
^{-1} = I
and
A
^{-1}
A = I
. For example, the
inverse of
A = |
A ^{-1} = |
=
and
= .
To find the inverse of an
m×m
matrix, write the
m×m
matrix on the left,
and the
m×m
identity matrix to the right:
Example: Find the multiplicative inverse of:
. |
. |