Direction : Consider the following for the items that follow :  

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

Let $A$ and $B$ be matrices of order $3 \times 3$. If $|A| = \frac{1}{2 \sqrt{2}}$ and $|B| = \frac{1}{729}$, then what is the value of $|2B(adj(3A))|$?

Consider the following statements in respect of two non-singular matrices $A$ and $B$ of the same order $n$:

1. 1.$adj(AB) = (adjA)(adjB)$


2. 2. $adj(AB) = adj(BA)$


3. 3. $(AB) adj(AB) - |AB| I_n$ is a null matrix of order $n$

Consider the following statements in respect of a non-singular matrix $A$ of order $n$:

1. $A(\text{adj}A^T) = A(\text{adj}A)^T$

2. If $A^2 = A$, then $A$ is identity matrix of order $n$

3. If $A^3 = A$, then $A$ is identity matrix of order $n$

Which of the statements given above are correct?