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A `2 xx 2` square matrix is written down at random using the number 1, -1 as elements. The probability that the matrix is non-singular is

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A 2×2 square matrix is written down at random using the number 1, -1 as elements. The probability that the matrix is non-singular is A. 1/2 B. 3/8 C. 5/8 D. 1/3 Select the correct answer from above options

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Correct Answer - A A 2 × 2 2 square matrix has 4 elements each of which can be chosen in 2 ways. ∴ ∴ Total number of 2 × 2 2 square matrices with elements 1 and -1 2 4 = 16 2 . Out of these 16 matrices, following matrices are singular : [ 1 1 − 1 − 1 ] , [ − 1 − 1 1 1 ] , [ 1 1 1 1 ] , [ − 1 − 1 − 1 − 1 ] [ [ − 1 1 1 1 ] , [ 1 − 1 1 − 1 ] , [ 1 − 1 − 1 1 ] , [ − 1 1 1 − 1 ] [ ∴ ∴ Number of non-singular matrices =16-8=8. Hence, required probability = 8 16 = 1 2 =

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