[Math] Adjacency matrix graphs and symmetry

Question

In an undirected graph, we have that the $a_{ij}$ entry in the adjacency matrix $A$ is equal to $1 \iff$ there is an edge between $i$ to $j$.

Now for undirected graphs we know that if there is an edge from $i \to j$ then this edge is also considered as an edge from $j \to i$.

Does that mean that $A$ will always be a symmetric matrix and that $A= A^T$ for all undirected graphs ?

I think the answer is true, But I just want to make sure If I am right or not

Answer 1

Yes, adjacency matrices for undirected graphs are symmetric.