Matrices And Determinants

If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a \(3 \times 3\) matrix \(\mathrm{A}\) and \(|\mathrm{A}|=4\), then \(\alpha\) is equal to