Inverse of a Matrix

Question

If A is as given below, then A^-1 exist if:
A=[(2,λ,-3)(0,2,5)(1,1,3)]

Answer 1

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.