I have the following square matrix to which I need to calculate it's determinant
A = \begin{matrix} 1 & 2 & 3 & ... & n \\ 1 & a+1 & 3 & ... & n \\ 1 & 2 & a+1 & ... & n \\ . & . & . & ... & . \\ . & . & . & ... & . \\ . & . & . & ... & . \\ 1 & 2 & 3 & ... & a+1 \\ \end{matrix} I have a strong feeling that this matrix can be reduced with some row operations to a triangular matrix and then the determinant will be a simple product of the prime diagonal.
Any suggestions?
Ri = Ri - R1 for each i>=2 realized it as soon as I posted it.