Is it possible to find determinant of a matrix by given the eigenvectors and the eigenvalues If I already found the eigenvalues and eigenvectors of a particular matrix , is there an easy way to find the  determinant of that matrix ? 

The formula is as follows
$\det(A) = \prod_{i=1}^N \lambda_i$,
where $\lambda_i$ is the $i^{th}$ eigenvalue of the matrix. The formula follows from the definition of the matrix characteristic equation $\det(A-\lambda I) = 0$. 
