Chapter 6.1, Problem 56E

Let $M_n$ be the $n\times n$ matrix with all 1‘s along “the otherdiagonal. and0’s everywhere else. For example, $M_4=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\\ 1& 0& 0& 0\end{array}\right]$ .
a. Find $\det \left(M_n\right)$ for $n=2,3,4,5,6,7$ .
b. Find a formula for $\det \left(M_n\right)$ , in terms of n.