Question

Compute the value of the determinant of the \(3 \times 3\) complex matrix \(X\), provided that \(\operatorname{tr}(X)=1, \operatorname{tr}\left(X^{2}\right)=-3, \operatorname{tr}\left(X^{3}\right)=4\). [Here \(\operatorname{tr}(A)\) denotes the the trace, that is, the sum of the diagonal entries of the matrix \(A .]\)