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KVPY SX SB Exam 2018 Question Paper

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Question : 17

Total: 120

Suppose A is a 3 × 3 matrix consisting of integer entries that are chosen at random from the set {–1000, –999, …, 999, 1000}. Let P be the probability that either A2=−I or A is diagonal matrix, (where I is the 3 × 3 identity matrix). Then

P<
1
1018
P=
1
1018
52
1018
≤P≤
53
1018
P≥
54
1018

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