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?