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Let n ge 2 be an integer, A=({:(cos((2pi...

Let `n ge 2` be an integer, `A=({:(cos((2pi)/(n)),sin((2pi)/(n)),0),(sin((2pi)/(n)),cos((2pi)/(n)),0),(0,0,1):})`
and I is the idnetity matrix of order 3. Then

A

`A^(n)=I " and " A^(n-1) ne I`

B

`A^(m) ne I` for any positive integer m

C

A is not invertible

D

`A^(m)=0` for a positive integer m

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Knowledge Check

  • The least positive integer n such that ({:(cos""((pi)/(4)),sin""((pi)/(4))),(-sin""((pi)/(4)),cos""((pi)/(4))):})^n is an identity matrix of order 2 is

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