Let A=left[a_{i j}right] be a square matrix of order 2 with entries either 0 or 1 . Let E be event t

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14.Probability

hard

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 $P ( E )$ is:

A$\frac{5}{8}$

B$\frac{3}{16}$

C$\frac{1}{8}$

D$\frac{3}{8}$

(JEE MAIN-2025)

Solution

C$-I$ $\left|\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right| \rightarrow 4$ ways
C$-II$ $\left|\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right| \&\left|\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right| \rightarrow 2$ ways
$P =\frac{\text { favourable }}{\text { total }}=\frac{6}{16}=\frac{3}{8}$

Standard 11

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