KCET2021MathematicsMatrices
If A and B are invertible matrices then which of the following is not correct ?
Options
- Aadj A=|A| A⁻¹
- Bdet (A⁻¹ )=[ det (A)]⁻¹
- C(A B)⁻¹=B⁻¹ A⁻¹
- D(A+B)⁻¹=B⁻¹+A⁻¹
Correct answer
D. (A+B)⁻¹=B⁻¹+A⁻¹
Step-by-step solution
If A and B are invertible matrices, then (a) (A B)⁻¹=B⁻¹ A⁻¹ (b) adj A=|A| A⁻¹ (c) |A⁻¹ |=|A|⁻¹ Hence, (A+B)⁻¹ B⁻¹+A⁻¹