While performing the hill cipher 2x2 (using mod 26), I'm having a bit of trouble determining what my final determinant should look like, because it's hard for me to find a number that I can multiply by my determinant to get 1 mod 26.
To find the determinant of a 2x2 Hill cipher matrix, you can use the formula:

determinant = (a * d) - (b * c)

where a, b, c, and d are the four elements of the matrix.

To find the multiplicative inverse of the determinant mod 26, you can use the Extended Euclidean Algorithm. If the determinant is not relatively prime to 26, then it does not have a multiplicative inverse mod 26, and the matrix is not invertible.

Assuming that the determinant has a multiplicative inverse mod 26, you can find it using the Extended Euclidean Algorithm. Once you have the multiplicative inverse, you can multiply it by the determinant to get 1 mod 26.

Note that if the determinant is even or a multiple of 13, then it is not relatively prime to 26 and does not have a multiplicative inverse mod 26. In this case, you will need to choose a different matrix for your Hill cipher.