How to use the function `Resolve` to verify this conclusion?

Let A be a non-zero square matrix of order n, $ A^{*}$ be the adjugate matrix of A, and $A^{T}$ be the transposition matrix of A. now we need to prove that when $ A^{*}=A^{T} $, $|A| neq 0$ always holds.

adj[m_] := 
 Map[Reverse, Minors[Transpose[m], Length[m] - 1], {0, 1}]*
  Table[(-1)^(i + j), {i, Length[m]}, {j, Length[m]}]
Resolve[ForAll[{M ∈ Matrices[{3, 3}, Reals]}, 
  M[Transpose] == adj[M], Det[M] != 0]]

The above code cannot verify this conclusion. What can I do to prove it?