JEE Mains · Maths · STD 11 - 14. probability
Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with entries either 0 or 1 . Let \(E\) be the event that \(A\) is an invertible matrix. Then the probability \(\mathrm{P}(\mathrm{E})\) is :
- A \(\frac{3}{16}\)
- B \(\frac{5}{8}\)
- C \(\frac{3}{8}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{8}\)
Step-by-step Solution
Detailed explanation
\(A=\left[a_y\right]_{2 \times 2}\) and entries are 0 or 1. \(\begin{aligned} & \therefore\left|\begin{array}{ll} a & b \\ c & d \end{array}\right|=0 \\ & \Rightarrow a d-b c=0 \end{aligned}\) Case I: \(a d=b c=1\) \(\therefore \quad a=b=c=d=1\) Case II: \(a d=b c=0\)…
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