Question bank/JEE Main/Mathematics

Let is a square matrix of order 2 where a_ij$\in$
then number of matrices A such that A^-1 exists is
$\lambda$ then $\lambda$- 300 is (given that all elements of matrix A
are distinct)

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For A^-1 exists $|A| \neq 0$
Case - I: Exactly one element is zero
Case - ll: No element is zero
$A = \left| \begin{matrix}
a\ \ \ \ b \\
c\ \ \ \ d
\end{matrix} \right|$
$|A|$= ad - bc = 0 ad = bc = 6 $\boxed{8}$
ad = bc = 12 $\boxed{8}$
$\Rightarrow \times \lfloor 4 - 16 = 120 - 16$
= 104
Total = 344

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx