Given an nn matrix with 0 or 1 as the value of each entry. We say the matrix is swappable if it is possible to interchange some of the pairs of rows and some of the pairs of columns so that, after all the interchanging, all the diagonal entries of the matrix are equal to 1.

(a) Provide an example of a matrix that is not swappable, but has at least one entry in each row and each column equal to 1.

(b) Provide an algorithm, which runs in polynomial time, to decide whether or not a matrix with 0-1 entries is swappable.