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 isA. `1//2`B. `3//8`C. `5//8`D. `1//3`

A `2 xx 2` square matrix is written down at random using the number 1,

1.	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 isA. `1//2`B. `3//8`C. `5//8`D. `1//3`
Answer» Correct Answer - A A `2 xx 2` square matrix has 4 elements each of which can be chosen in 2 ways. `therefore` Total number of `2xx2` square matrices with elements 1 and -1 `2^(4)=16`. 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]]` `therefore` Number of non-singular matrices =16-8=8. Hence, required probability `=(8)/(16)=(1)/(2)`

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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 isA. `1//2`B. `3//8`C. `5//8`D. `1//3`

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