# Find the inverse of 3X3 matrix (mod 19)

• Nov 18th 2012, 03:31 AM
ScorpFire
Find the inverse of 3X3 matrix (mod 19)
I have been trying to find the inverse matrix of the following matrix (mod 19)

$A = \begin{bmatrix} 1 & 14 & 9 \\ 7 & 15 & 8 \\ 2 & 13 & 4\end{bmatrix} mod 19.$.

I used gauss-jordan elimination method (i.e. augment A with identity matrix, and reduce the left matrix to an identity matrix) and its very tedious. Everytime i change an element, another element of the same row gets affected then i have to go back and redo all over.

Is there an efficent way to do this? Thanks in advance for your help.
• Nov 18th 2012, 04:51 PM
chiro
Re: Find the inverse of 3X3 matrix (mod 19)
Hey ScorpFire.

Take a look at this:

Finite Fields Calculations - Newsreader - MATLAB Central
• Nov 18th 2012, 04:59 PM
Deveno
Re: Find the inverse of 3X3 matrix (mod 19)
you shouldn't have to "start all over".

i recommend gauss-jordan (row-reduction) in this order:

12R1 + R2
8R2
17R1 + R3
5R2 + R1
6R2 + R3
16R3
3R3 + R2
6R3 + R2 <---you should be done at this point.

remember to reduce mod 19 after each step (to keep the numbers you're working with small).