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Random 2x2 matrix with entries from a set: probability it is singular or invertible

This type of question, asked 3 times: 29 Jun 2022, 11 Apr 2023, 24 Jan 2025. All 3 questions below, oldest first.

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  1. Question 1

    29 Jun 2022

    61
    The probability that a randomly chosen 2×22 \times 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to:

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  2. Question 2

    11 Apr 2023

    70
    Let S={M=[aij],aij∈{0,1,2},1≤i,j≤2}S =\left\{ M =\left\lbrack a_{ij} \right\rbrack,a_{ij}\mathbf{\in \{ 0,1,2\},1 \leq i,j \leq 2} \right\} be aa sample space and A={M∈S:M\mathbf{A = \{ M \in S:M} is invertible }\} be an event. Then P(A)P(A) is equal to

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  3. Question 3

    24 Jan 2025

    144
    Let A=[aij]A=\left\lbrack a_{ij} \right\rbrack be a square matrix of order 2 with entries either 0 or 1 . Let E be the event that A is an invertible matrix. Then the probability P(E)P(E) is :

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