(Solved): A graph with vertices \( A, B, C, D \) has the following adjacency matrix denoted \( M \) (with ro ...

A graph with vertices \( A, B, C, D \) has the following adjacency matrix denoted \( M \) (with rows and columns in the order \( A, B, C, D) \) \[ M=\left[\begin{array}{llll} 1 & 1 & 0 & 1 \\ 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 1 & 0 & 1 & 0 \end{array}\right] \] (a) Which of the following are true? Select all that apply. A. Vertices \( C \) and \( A \) are adjacent B. Vertices \( A \) and \( D \) are adjacent C. Vertices \( A \) and \( B \) are adjacent D. There is an edge from vertex \( D \) back to itself (b) Calculate \( M^{3} \) : (c) How many walks are there from vertex \( C \) to vertex B using exactly 3 edges?