we know, inverse of any matrix a is possible only when a is non - singular matrix.
i.e., |a| ≠ 0
so, determinant of a , |a| = 2(2 × 3 - 5 × 1) - λ(0 × 3 - 1 × 5) + (-3) (1 × 0 - 1 × 2) ≠ 0
or, 2(6 - 5) + 5λ + 6 ≠ 0
or, 5λ + 8 ≠ 0
or, λ ≠ -8/5
hence value of λ is all real numbers except x = -8/5 .
so, option (1) is correct choice.