Matrix array built from range?

Question

I have the problem on a past exam:

Let the array $L$ be defined by: $0\leq i, j \leq n-1$

$$L=[l_{i,j}] \text{where } l_{i.j} \equiv i+j \pmod n$$

Let $n=4$ and write down the array $L=[l_{i,j}]$

(This appeared to me to be a latin square problem) Now my problem lies in the $i$ range I suppose and that I thought $n=4$ meant I would have a latin square of side $n$, and hence an $4\times 4$ array, but with $j\leq n-1$ I seem to have three as one side.

So in my attempt to construct this I got:

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

Which I don't feel is correct based on $n=4$

Question: Why does this seem to not be $4\times 4$, and what does $0 \leq i$ mean here?

Is this correct?

Answer 1

I think here the indices $i$ and $j$ start from $0$, ${i.e.}$,

$$ L = \begin{bmatrix} l_{0, 0} & \cdots & l_{0, n-1}\\ \vdots & \ddots & \vdots\\ l_{n-1, 0} & \cdots & l_{n-1, n-1} \end{bmatrix}. $$

Therefore, the matrix is

$$ L = \begin{bmatrix} 0 & 1 & 2 & 3\\ 1 & 2 & 3 & 0\\ 2 & 3 & 0 & 1\\ 3 & 0 & 1 & 2 \end{bmatrix}. $$