AP EAMCET202420 May 2024Evening ShiftMathematicsMatricesActual
Let A , B , C , D and E be n n matrices, each with non-zero determinant. If ABCDE = I , then C ⁻¹=
Options
- AE ⁻¹ D ⁻¹ ~B ⁻¹ ~A ⁻¹
- BDEAB
- CA ⁻¹ ~B ⁻¹ D ⁻¹ E ⁻¹
- DABDE
Correct answer
B. DEAB
Step-by-step solution
ABCDE = I A ⁻¹ ABCDE = A ⁻¹ aligned & BCDE = A ⁻¹ CDE = B ⁻¹ ~A ⁻¹ & CD = B ⁻¹ ~A ⁻¹ E ⁻¹ C = B ⁻¹ ~A ⁻¹ E ⁻¹ D ⁻¹ & C ⁻¹= DEAB aligned