# Matrix of Primes

$\large {\begin{bmatrix} 3 & 5 \\ 2 & 7 \end{bmatrix}}$

Above is a $$2 \times 2$$ matrix having elements from the set of first $$4$$ prime numbers i-e $$S= \left\{ 2,3,5,7 \right\}$$ such that they may or may not repeat.

For how many ordered tuples $$T(w,x,y,z)$$, where $$w,x,y,z$$ belongs to the set $$S$$, determinant of the matrix $$M=\begin{bmatrix} w & y \\ x & z \end{bmatrix}$$ is also prime ?

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