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

Options

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

Answer

A

Explanation

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)`