# matrix – 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?