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

#### swiftshift

find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is

Last edited:

#### kaelbu

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?

• Sudharaka, HallsofIvy and swiftshift

#### Sudharaka

find the inverse of

1 2 -3
3 2 -1
2 1 3

if there is
Dear swiftshift,

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

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

Last edited:
• swiftshift

#### swiftshift

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

#### HallsofIvy

MHF Helper
Dear swiftshift,

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

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!

• Sudharaka