Thread: Matrices Question

Hi, can someone please help me with this question:

Let K be the finite field with only the two elements 0 and 1, where 1+1=0
(i) How many 2x2 matrices with entries in K are there?
(ii) How many of these are non singular?


I understand that the question is refering to the field Z(integers) mod 2, but I'm not sure how that relates the matrices in question


Thank you!!

Originally Posted by pseudonym

Hi, can someone please help me with this question:

Let K be the finite field with only the two elements 0 and 1, where 1+1=0
(i) How many 2x2 matrices with entries in K are there?
(ii) How many of these are non singular?


I understand that the question is refering to the field Z(integers) mod 2, but I'm not sure how that relates the matrices in question


Thank you!!

1. $\displaystyle 2^4$.
2. $\displaystyle (2^2 - 1)(2^2 - 2) = 6$. See here.