Verified Solution • 2025–26 Session moderate

QJEEM25Ma5e34: JEE Main 2025 Mathematics - Class 12 JEEM25Ma5e34 Solution: Let be a square matrix of order 2 with entries either 0 or 1 .…

Let A=[aij]\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\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)\mathrm{P}(\mathrm{E}) is :

Multiple Choice Options

  • A 38\frac{3}{8}
  • B 18\frac{1}{8}
  • C 316\frac{3}{16}
  • D 58\frac{5}{8}

Step-by-Step Verified Solution

C-I ∣1amp;10amp;1∣→4\left|\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right| \rightarrow 4 ways

C-II ∣1amp;00amp;1∣&∣0amp;11amp;0∣→2\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= favourable  total =616=38\mathrm{P}=\frac{\text { favourable }}{\text { total }}=\frac{6}{16}=\frac{3}{8}

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