If A = (\table1/\sqrt5,2/\sqrt5;-2/\sqrt5,1/\sqrt5), B = (\table 1,0;i,1), i = \sqrt{-1} , and \Q=\A^{\T} \B \A, then the inverse of the matrix \A \Q^{2021} \A^{\T} is equal to [26 Aug 2021 Shift 1]

Correct Answer is : (10−2021i1)

(\table 1/\sqrt5,-2021;2021,1/\sqrt5)

JEE Main 26-Aug-2021 Shift 1 Solved Paper

Section: Mathematics

Question : 76 of 90

Marks: +1, -0

If A = (

√5

−

√5

), B = (

1	0
i	1

), i=√−1 , and Q=ATBA, then the inverse of the matrix AQ2021AT is equal to

[26 Aug 2021 Shift 1]

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1	0
−2021i	1

1	0
2021i	1

1	−2021i
0	1

1	0
2021i	1