Chapter 4.2, Problem 23E

Let $A=(a_{ij})$ be the $(n\times n)$ matrix specified thus: $a_{ij}=d$ for $i=j$ and $a_{ij}=1$ for $i\ne j$. For $n=2,3,\text{ and 4, }$ show that $\det (A)={(d-1)}^{n-1}(d-1+n)$.