Question

# 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. ThenP<11018P=11018P≥541018521018≤P≤531018

Solution

## The correct option is A P<11018Given : A2=−I Taking determinant, |A|2=−1 which is not possible so, A is diagonal matrix  Now the total possible matrix =20019 Number of diagonal matrix =20013 So, P=2001320019=120016 ∴P<120006<110006<11018

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