Jee Main 2025 — Medium JEE math MCQ
If $A, B,$ and $(\text{adj} (A^{-1}) + \text{adj} (B^{-1}))$ are non-singular matrices of same order, then the inverse of $A (\text{adj} (A^{-1}) + \text{adj} (B^{-1}))^{-1} B$, is equal to
- A. $AB^{-1} + A^{-1}B$ -
- B. $\text{adj} (B^{-1}) + \text{adj} (A^{-1})$ -
- C. $\frac{AB^{-1}}{|A|} + \frac{BA^{-1}}{|B|}$ -
- D. $\frac{1}{|A|}(\text{adj}B. + \text{adj}(A))$
Solution
The correct option is **D**. (D. $\frac{1}{|A|}(\text{adj}B. + \text{adj}(A))$)