Discuss the validity of the following statement. If the statement is always true, explain why. If not, give a counterexample. If the 2 times 2 matrix P is the transition matrix for a regular Markov chain, then, at most, one of the entries of P is equal to 0. Choose the correct answer below. A. This is false. In order for P to be regular, the entries of P^k must be non-negative for some value of k. For k=1 the matrix Start 2 By 2 Table 1st Row 1st Column 0 2nd Column 1 2nd Row 1st Column 0 2nd Column 1 EndTable has non-negative entries and has two zero entries. Thus, it is a regular transition matrix with more than one entry equal to 0. B. This is true. If there is more than one entry equal to 0, then the number of entries equal to zero will increase as the power of P increases. C. This is true. If there is more than one entry equal to 0, all powers of P will contain 0 entries. Hence, there is no power k for which Upper P Superscript k contains all positive entries. That is, P will not satisfy the definition of a regular matrix if it has more than one 0. D. This is false. The matrix P must be regular, which means that P can only contain positive entries. Since zero is not a positive number, there cannot be any entries that equal 0.