Test Index

CBSE Class 12 Math 2025 All Sets Solved Paper

© examsnet.com
Question : 17 of 20
Marks: +1, -0
If A and B are invertible matrices, then which of the following is not correct?
Solution:  
Since A&BA \& B are invertible matrix, so we can say that
(AB)−1=B−1A−1(A B)^{-1}=B^{-1} A^{-1}
Also, A−1=1∣A∣(adjA)A^{-1} = \frac{1}{|A|} \left( \frac{\mathrm{adj}}{A} \right)
⇒adj(A)=∣A∣⋅A−1\Rightarrow \mathrm{adj}(A) = |A| \cdot A^{-1}
∣A−1∣=1∣A∣|A^{-1}| = \frac{1}{|A|}
∣A−1∣=∣A∣−1|A^{-1}| = |A|^{-1}
Now, (A+B)−1=1∣A+B∣adj(A+B)(A+B)^{-1} = \frac{1}{|A+B|} \mathrm{adj}(A+B)
⇒(A+B)−1≠A−1+B−1\Rightarrow (A+B)^{-1} \neq A^{-1}+B^{-1}
This statement is not true. The inverse of a sum of matrices is not equal to the sum of their inverse.
© examsnet.com
Go to Question:
Prev Question
Next Question