Chapter 6.2, Problem 65E

Let $M_n$ be the $n\times n$ matrix with 1‘s on the main diagonal and directly above the main diagonal, $-1\text{'}\text{s}$ directlybelow the main diagonal, and 0’s elsewhere. Forexample,
$M_4=\left[\begin{array}{cccc}1& 1& 0& 0\\ -1& 1& 1& 0\\ 0& -1& 1& 1\\ 0& 0& -1& 1\end{array}\right]$ .
Let $d_n=\det \left(M_n\right)$ .
a. For $n\ge 3$ , find a formula expressing 4 in terms of $d_{n-1}$ and $d_{n-2}$ .
b. Find $d_1,d_2,d_3,d_4$ , and $d_{10}$ .
e. For which positive integers n is the matrix $M_n$ invertible?