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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. Then
  1. P<11018
  2. P=11018
  3. P541018
  4. 521018P531018


Solution

The correct option is A P<11018
Given :
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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