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Question

A second order determinant is written down at random using the numbers 1, - 1 as elements. The probability that the value of the determinant is non zero is

A
12
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B
38
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C
58
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D
18
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Solution

The correct option is A 12
Let S be the set of second order determinants formed using 1 and -1 as elements. n(S)=24=16 (because each of the four places can be filled in 2 ways). The zero determinants are
1111,1111,1111,1111,1111,1111,1111,1111
n(E) = 8
P(E)=n(E)n(S)=816=12

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