Q:

Give an example of a singular matrix in $M_{3×3}(Q)$ the entries of which are distinct prime positive integers, or show that no such matrix can exist. 

I know that the matrix exist because the entries are primes but I don´t know how to explain, i need some help. 
Give an example of a singular matrix in $M_{3×3}(Q)$ the entries of which are distinct prime positive integers, or show that no such matrix can exist. 

A:

$$\pmatrix{5&7&11\cr17&19&23\cr41&43&47\cr}$$ EDIT: Also, but not obvious,  $$\pmatrix{2&3&5\cr7&11&13\cr17&19&101\cr}$$

A:

With the first $9$ primes you get the following examples which are not equivalent under row or column permutations:
$$\left[\matrix{2&19&13\cr 11&3&5\cr 7&23&17\cr}\right],\quad
\left[\matrix{2&19&5\cr 11&3&17\cr 7&23&13\cr}\right],\quad
\left[\matrix{2&5&3\cr 13&7&11\cr 17&23&19\cr}\right]\ .$$
Here is another one, obtained from choosing randomly $9$ from the first $60$ primes:
$$\left[\matrix{13&191&163\cr 31&137&151\cr 17&271&229\cr}\right]\ .$$

A:

There should be simpler examples using smaller primes, but you may fill the matrix with nine primes from CPAP-9 to get a rank-2 matrix.  See also the related question: Special matrices with determinant 0.