Find determinant of matrix A \begin{bmatrix} a+b & ab & 0 & ... & 0\\ 1 & a+b & ab & ... & 0\\ 0 & 1 & a+b & ... & 0\\ ... & ... &... & ... &...\\ 0 & 0 & 0 &... & a+b \end{bmatrix}
Let's say shape is $N\times N$.
It seems $(a+b)\cdot row_{i} - row_{i+1}$ for i from 1 up to N-1
So in case $a+b \neq 0$ and $n>1$ we have: $det(A) = \frac{((a+b)^2 - ab)^{n-1}}{(a+b)^{n-1}}\cdot(a+b) = \frac{(a^2 + ab + b^2)^{n-1}}{(a+b)^{n-1}}\cdot(a+b)$
Where is a mistake? I don't get right result in case $n>2$ ...
Thank you
