2. ## Re: How can i prove that about Det(a1,…,an)?

Try using Gaussian elimination to transform this matrix to an upper diagonal one. Then read the determinant off as the product of the diagonal elements.

3. ## Re: How can i prove that about Det(a1,…,an)?

some hints

Look at the matrix $B=A-xI$ where $I$ is the $n\times n$ identity matrix

the characteristic polynomial of $B = det(B-xI)$

$B$ is a rank one matrix