I was reading this Transversal of Primes, and the solution shown for an $11 \times 11$ grid. Made me think of an identity matrix.
First, have each $a_{ij}$ be either $1$ for a prime number or $0$ otherwise. then the $11$ primes will "map" to the identity matrix. (for $GL_{11}(\mathbb{R})$)?
I am asking to help clarify my own knowledge, I have started learning a bit of Abstract Algebra and reviewing Linear Algebra (because my TI-89 made class to easy).
Also, are there any other Prime Identity matrices, which can "map" to an identity matrix? I haven't found a good way of computing the distance between each prime number corresponding to the location in the matrix, still working on that.
*Please edit to make better, I admit this may be an awkward question.
EDIT to make the question more self-contained: a "transversal of primes" is obtained by writing the numbers from $1$ to $p^2$ ($p$ a prime) in their natural order in a $p\times p$ grid and then choosing primes in such a way that you choose exactly one number from each row and from each column. The link gives an example for $p=11$ and asks whether there is such a transversal for every prime $p$. For $p=3$, we're talking about the grid $\matrix{1&2&3\cr4&5&6\cr7&8&9\cr}$ and $3, 5, 7$ is a transversal of primes.