Let X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct?

I. (ZY)X is defined and is a square matrix of order 3.

II. Y(XZ) is defined and is a square matrix of order 2.

III. X(YZ) is not defined.

Select the answer using the code given below.

Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct? 

Consider the following in respect of the matrices  $\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}$

I. PQ is a null matrix. 

II. QP is an identity matrix of order 3. 

III. PQ = QP

Which of the above is/are correct? 

Direction : Consider the following for the items that follow :  

Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$

What is A(adj A) equal to?