Most Important Selected Qs for JEE AdvancedMathematicsMatrices
If A is an invertible matrix then ( adj A )⁻¹=
Options
- Aadj ( A ⁻¹ )
- BA det A
- CA
- D( det A ) A
Correct answer
B. A det A
Step-by-step solution
A ( adj A )=| A | I =( adj A ) A ( adj A )⁻¹ ~A ⁻¹= I | A | = A ⁻¹( adj ~A )⁻¹ ...(i) aligned & taking Inverse & Also & A ⁻¹ ( adj ~A ⁻¹ )= | A ⁻¹ | . I aligned A ⁻¹ ( adj ~A ⁻¹ )= 1 | ~A | I ....(ii) aligned & A ⁻¹ ( adj ~A ⁻¹ )= A ⁻¹( adj ~A )⁻¹ from ( i ) &( ii ) & ( adj A ⁻¹ )=( adj A )⁻¹ option ( B ) is correct. & A ( adj A )=| A | I aligned A | A | ( adj A )= I ( adj A )⁻¹= A | A | Option (A) is correct.