A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is
Total number of determinants of order \(2 \times 2\), which can be formed by using 1 and 0 only is \(2 \times 2 \times 2 \times 2=16\) Non zero determinants are \[\] \(\left|\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right|,\left|\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right|,\left|\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right|\), \[\] \(\left|\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right|,\left|\begin{array}{ll}1 & 1 \\ 1 & 0\end{array}\right|,\left|\begin{array}{ll}0 & 1 \\ 1 & 1\end{array}\right|\) \[\] Required probability is \(\frac{6}{16}=\frac{3}{8}\) Choice (B)
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