IB Maths AI HL AI 1.5 Matrices questions

A field station sends four-letter locker identifiers using a linear code. The letters A to Z are represented by the integers 1 to 26, respectively. Each successive pair of letters is written as a column vector $\mathbf{x}$ and is encoded as $\mathbf{y}=K\mathbf{x}$

The transmitted pairs, in order, are

$$\begin{pmatrix}27\\14\end{pmatrix} \quad\text{and}\quad \begin{pmatrix}48\\28\end{pmatrix}.$$

The same encoding matrix was used for both pairs. It was one of

$$P=\begin{pmatrix}2&1\\1&1\end{pmatrix} \quad\text{or}\quad Q=\begin{pmatrix}1&2\\1&3\end{pmatrix}.$$