Rank is an important property of a matrix, used in many mathematical and scientific applications. The rank of a matrix A is the maximum number of linearly independent columns of A; or, it is the order of the largest nonsingular matrix contained in A. Find the rank of the following matrices:

(a) A = [3,2; 6,1; 3,0],

(b) B = [2,4,0,8; 1,2,6,3],

(c) C = [3,0,0; 1,2,0; 0,0,1]

(Hint: Use the MATLAB inbuilt function rank)

If matrix A = [3, 9, 2; 1, 3, 0; 2, 6, 1], verify the following properties:

(a) Rank of A = rank of A'

(b) Rank of A = rank of A'A

(c) Rank of A = rank of AA'