Part CCSIR NET December 2023order-of-gl2-over-z-9

Order of gl2 over z 9

Let G be the group (under matrix multiplication) of 2 × 2 invertible matrices with entries from $Z /9 Z$ . Let a be the order of G. Which of the following statements are true?

A.a is divisible by $3^{4}$ .
B.a is divisible by $2^{4}$ .
C.a is not divisible by 48.
D.a is divisible by $3^{6}$ .

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The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Every group of order p² is cyclic

Order of gl2 over z 9

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