### Matrix Permutations

Hello,

how do I get all permutations of a Matrix?

For the following exercise I would like to get all permutations of a Matrix with integer values in the range $0$ to $9$. There should be $10^4$ permutations. And then generate the permutations of tuples with three matrices. $10^{12}$ permutations and then I would filter the list somehow for the invertible matrices.

Is there a better way?

Exercise:
Let $S, T, U \in \mathbb{R}^{2x2}$ such that, $S_{i, j}, T_{i, j}, U_{i, j} \in {0,1, \cdots, 9}$
How many of the products $S \cdot T \cdot U$ are invertible?

In the Sage reference for permutation I couldn't find any thing.

Thanks

PS: The curly braces couldn't be escaped properly in the LaTex part ... \{0,1, \cdots, 9\}