# Thread: Finding inverse of a matrix (A^-1)

1. ## Finding inverse of a matrix (A^-1)

find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is

2. ## how to find the inverse

The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
So
1 2 -3 | 1 0 0
3 2 -1 | 0 1 0
2 1 3 | 0 0 1

Does that help?

3. Originally Posted by swiftshift
find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is
Dear swiftshift,

$\left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array }{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left( \begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\r ight)$

By matrix multiplication you could obtain nine equations and solve for the unknowns.

4. Originally Posted by kaelbu
The inverse can be found by setting this matrix equal to the identity matrix and row reducing so that the identity matrix is on the other side of equal sign (the inverse matrix will be where the identity matrix is originally).
So
1 2 -3 | 1 0 0
3 2 -1 | 0 1 0
2 1 3 | 0 0 1

Does that help?
thanks mate

5. Originally Posted by Sudharaka
Dear swiftshift,

$\left(\begin{array}{ccc}1&2&-3\\3&2&-1\\2&1&3\end{array}\right)\times\left(\begin{array }{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right)=\left( \begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\r ight)$

By matrix multiplication you could obtain six equations and solve for the unknowns.
Actually, you get nine equations for the nine unknowns. Probably not the best way to find an inverse!