Exercise · ZW-ORDER-OF-A-GROUP-008 · ★★☆ Intermediate
How many elements does the group \(GL_2(\mathbb{Z}_2)\) of invertible \(2\times2\) matrices with entries in \(\mathbb{Z}_2\) have?
Choose one option.
Show answer
- C. 6
Explanation
There are \(2^4=16\) matrices, but only those with determinant \(1\) mod 2 are invertible, and listing them gives 6. The 16 include the singular ones.
Review the concept: Order of a group
The order of a finite group \(G\) is its number of elements; if \(G\) is infinite it has infinite order.
\[|G|\]
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