Which one can be accompanied by linear filters?

I have a matrix :

$$\begin{bmatrix} 1 & 2 & 3\\ 1 & 4 & 5\\ 2 & 6 & 7 \end{bmatrix}$$

After doing operation 1 , I get

$$\begin{bmatrix} 0 & 0 & 0\\ 1 & 2 & 3\\ 1 & 4 & 5 \end{bmatrix}$$

However operation 2 on same matrix will give : $$\begin{bmatrix} 0 & 1 & 2\\ 0 & 3 & 4\\ 1 & 5 & 6 \end{bmatrix}$$

Clearly, operation 2 reduces each matrix value by 1, while operation 1 shifts one row down.

Now I see that operation 1 is simply subtraction and thus can be applied using linear filter. But I am not using to linear filters on matrix. Can anyone guide me through this?

TL;DR: Time shift in doable with LTI systems. Subtracting $$1$$ is non linear.