"an" vs "a" special case

[hodorhodor]

Hello,

I was studying for my final exam yesterday when I came across the following:
"take the determinant of a NxN matrix" (for those unsure it is pronounced "N by N matrix"). Now my question is the following: is the use of "a" here grammatically correct?

I know that the trick for an vs a depends on the starting sound of the following word, and not necessarily on whether the word starts with a vowel or a consonant, but this sounded wrong to my ear when I said it out loud and got me really confused. Pronouncing the letter N on its own sounds more like "an" or "èn", similar to the pronunciation of "animal" (AN animal). I asked a bunch of my friends who are native English speakers and they said the way it is written is correct, but I am not completely convinced.

So here I am procrastinating, and asking if anyone would be kind enough to help me solve this useless conflict that has been keeping me from focusing on what's really important.

[Joe]

If "NxN matrix" is pronounced "en by en matrix", then you are absolutely correct:

an NxN matrix

[Joe]

When we say the letter N, we say "en". That is, we start with a vowel sound /e/. So the a/an determiner is "an":

When to Say a or an
https://www.englishclub.com/pronunciation/a-an.htm

[Joe]

If, on the other hand, you wanted to talk about a TxT matrix, then "a" would be correct. The letter T is pronounced "tee" and starts with a consonant sound /t/.