Does there exist a square matrix with 32 elements ?

Consider an arbitarary 3xx3 non-singular matrix A[a_("ij")] . A maxtrix B=[b_("ij")] is formed such that b_("ij") is the sum of all the elements except a_("ij") in the ith row of A. Answer the following questions : If there exists a matrix X with constant elemts such that AX=B , then X is

If A^(T) is the transpose of a square matrix A, then

Which of the following is (are) NOT the square of a 3xx3 matrix with real entries ?

If the matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?

If A is a square matrix then find the odd man out:

Suppose that matrix has 8 elements.What are the possible orders it can have?What if it has 11 elements?