Thus if two matrices are equal then the graphs corresponding to those matrices are Isomorphic.
This statement is true. However, adjacency matrix and incidence matrix can be used in order to verify an isomorphism, rather than finding one. This is because when we write an adjacency matrix of two graphs that are isomorphic, if the ordering of vertices in matrix representations is not the same, then we probably get a different matrix. But, if we have an isomorphism between two graphs $G$ and $H$, say $\phi: G \to H$, with $V(G) = \{v_1,v_2,...,v_n\}$ and $V(H) = \{u_1, u_2,...,u_n\}$ then the ordering in adjacency matrices of these graphs should be like $(v_1,...,v_n)$ and $(\phi(v_1),...,\phi(v_n))$. Here, note that there might be more than one isomorphism and we may get the same matrices with different orderings.
In summary, if we can define a function $\phi: G \to H$ and suspecting that $\phi$ is an isomorphism, then we can verify it by comparing the matrices with orderings $(v_1,...,v_n)$ and $(\phi(v_1),...,\phi(v_n))$. If this is the case, matrices being the same proves that $\phi$ is an isomorphism.
