Find the inverse of 3X3 matrix (mod 19)

I have been trying to find the inverse matrix of the following matrix (mod 19)

$\displaystyle 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.

Re: Find the inverse of 3X3 matrix (mod 19)

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).