Impossible hill cipher question I've been trying to solve this question from Forouzan's book (&quot;Cryptography And Network Security&quot;) and haven't been able to wrap my head around how to solve it.

The plaintext “letusmeetnow” and the corresponding ciphertext
“HBCDFNOPIKLB” are given. You know that the algorithm is a Hill
cipher, but you don’t know the size of the key.
Find the key matrix.

I inverse the 2x2 plaintext matrix and multiple with a 2x2 ciphertext matrix and take a mod 26. However, the key matrix is always in fractions, never an integer.
It would be great if someone could point me in the right direction / tell me what I'm doing wrong.
Thanks in advance!
Two independent ideas:

In the Hill cipher, elements of matrices are in the ring of integers modulo the number of characters in the alphabet used, usually $n=26$. Therefore, as long as the denominator of a fraction is coprime with $n$ (that is, for $n=26$, if the denominator is divisible neither by $2$ not by $13$), that fraction reduces to an integer modulo $n$.E.g. $\displaystyle\frac23\equiv18\pmod{26}$ since $2\equiv3\cdot18\pmod{26}$.
The Hill cipher is sometime instantiated with a $3\times3$ or larger matrix.