$B=((b_{ij}))$ where $b_{ij}=1 \, \forall i,j$ and $A=(a-b)i_n+bB$ Prove that $|A|=(a-b)^{n-1}[a+(n-1)b]$
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix