The least positive integer n such that (\table \cos\pi/{4},\sin\pi/{4};-\sin\pi/{4},\cos\pi/{4})^n is an identity matrix of order is

WBJEE 2018 Math Solved Paper

Question : 62 of 75

Marks: +1, -0

The least positive integer n such that (

cos

sin

−sin

cos

)n is an identity matrix of order is

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λ	λ
−λ	λ

λ	λ
−λ	λ

λ	λ
−λ	λ

0	2λ2
−2λ2	0

0	2λ2
−2λ2	0

0	2λ2
−2λ2	0

−4λ4	0
0	−4λ4