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?

How many four-digit natural numbers are there such that all of the digits are even?

If $\omega \neq 1$ is a cube root of unity, then what are the solutions of $(z-100)^3 + 1000 = 0$?