1. The problem statement, all variables and given/known data
[tex]
\begin{pmatrix}
5 & 8\\
17 & 3\\
\end{pmatrix}
[/tex]
The matrix given above is matrix A and I am trying to find A-1 mod 26 = ?
2. Relevant equations
ax+by = c
3. The attempt at a solution
Well first I found the det of A which is -121 and then took -121 modulus of 26 which gave me 9. Did I do the work that I UPLOADED for this part right? After that I set -121 = 9 mod 26. So now to find the inverse, I need the Euclidean algorithm, an here is where I get lost. First I put the mod number on the let of the equals sign then I multiplied 9 by some number not known yet and added some remainder. By dividing 26 by 9 I get that the number is 2 and the remainder is 8. Now I move 9 to replace 26 on the left and 8 to replace 9 on the left and a new unknown remainder. Now 8 goes into 9 once with a remainder of 1. Finally 8 will now move to the left and 1 will replace 1. Now if I divide 8 by 1 I get 8 so the number will be 8 with a 0 remainder. If this is confusing please use my UPLOADED WORK. All in all the equations will be:
26 = 9(2) + 8
9 = 8(1) + 1
8 = 1(8) + 0
My question is did I do it correctly or what did I do wrong?
[tex]
\begin{pmatrix}
5 & 8\\
17 & 3\\
\end{pmatrix}
[/tex]
The matrix given above is matrix A and I am trying to find A-1 mod 26 = ?
2. Relevant equations
ax+by = c
3. The attempt at a solution
Well first I found the det of A which is -121 and then took -121 modulus of 26 which gave me 9. Did I do the work that I UPLOADED for this part right? After that I set -121 = 9 mod 26. So now to find the inverse, I need the Euclidean algorithm, an here is where I get lost. First I put the mod number on the let of the equals sign then I multiplied 9 by some number not known yet and added some remainder. By dividing 26 by 9 I get that the number is 2 and the remainder is 8. Now I move 9 to replace 26 on the left and 8 to replace 9 on the left and a new unknown remainder. Now 8 goes into 9 once with a remainder of 1. Finally 8 will now move to the left and 1 will replace 1. Now if I divide 8 by 1 I get 8 so the number will be 8 with a 0 remainder. If this is confusing please use my UPLOADED WORK. All in all the equations will be:
26 = 9(2) + 8
9 = 8(1) + 1
8 = 1(8) + 0
My question is did I do it correctly or what did I do wrong?
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