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 :

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Aicharya · Accepted Answer

$A=\left[a_yight]_{2 	imes 2}$ and entries are 0 or 1. $\begin{aligned} & 	herefore\left|\begin{array}{ll} a & b \ c & d \end{array}ight|=0 \ & \Rightarrow a d-b c=0 \end{aligned}$ Case I: $a d=b c=1$ $	herefore \quad a=b=c=d=1$ Case II: $a d=b c=0$ $\begin{array}{ll} a=0, d=0 & b=0, c=0 \ a=0, d=1 & b=0, c=1 \ a=1, d=0 & b=1, c=0 \end{array}$ $	herefore$ Total 10 cases when matrix is non invertible Total possible matrix $=2^4=16$ Required probability of invertible $=\frac{16-10}{16}=\frac{6}{16}=\frac{3}{8}$ ~

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…

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