MHT CET202521 Apr 2025Evening ShiftMathematicsMatricesActual
Let A be a non-singular matrix of order n and |A|=k , then ( adj A)⁻¹ is
Options
- AA k
- Bk ^ n -1 ( adj ~A )
- Ck ^ n -2 ~A
- DkA
Correct answer
A. A k
Step-by-step solution
A non-singular matrix A of order n with |A|=k satisfies the fundamental relationship adj A = |A| A⁻¹ = k A⁻¹ . The inverse of adj A is then given by ( adj A)⁻¹ = (k A⁻¹)⁻¹ = 1 k (A⁻¹)⁻¹ = 1 k A . This result corresponds to option A , A k .