# Matrices Question

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• March 2nd 2010, 03:09 PM
pseudonym
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!!
• March 3rd 2010, 12:56 AM
aliceinwonderland
Quote:

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