Calculate the determinant of the matrix which is a+b when i=j, and a otherwise

Calculate the determinant of the matrix which is a+b when i=j, and a
otherwise

the matrix is n x n , defined as the following:
ai,j = {a+b: when i=j , a: when i is not equal to j .
when I calculated it I got the answer of: b^n +nab^n-1 , but I saw other
solution that said the answer is b^n + ab^n-1, so I'm not sure. Can you
tell me the right solution and show me the steps to calculate it if I'm
wrong ? thank you.