Let A=[a_ij] be a square matrix of order 2 with entries either 0 or 1 .

Question

Let $A=[{a}_{ij}]$ 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 :

Accepted Answer

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

$$\mathrm{P}=\frac{\text { favourable }}{\text { total }}=\frac{6}{16}=\frac{3}{8}$$

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