NDA 2016
- Exam
- NDA
- Year
- 2016
- Subject
- Mathematics
- Chapter
- Matrices
NDA 2016 · Mathematics · Matrices
A= [ array rr 1 & -1 2 & 3 array ] and B=[ array rr 2 & 3 -1 & -2...
\left[\right]B=\left[\right]\quad \mathrm{AB} \left(\mathrm{A}^{-1} \mathrm{ B}^{-1}\right)( \mathrm{AB})^{-1}=\mathrm{A}^{-1} \mathrm{ B}^{-1} Select the correct answer using the code given below:
Options
- A1 only
- B2 only
- CBoth 1 only 2
- DNeither 1 nor 2
Correct answer
D. Neither 1 nor 2
Step-by-step solution
Here, A=\left[\right] and B=\left[\right]|A|=3-(-2)=5 and |B|=-4-(-3)=-1\Rightarrow A^{-1}=\frac{1}{5}\left[\right] and B^{-1}=-1\left[\right]A B=\left[\right] and A^{-1} B^{-1}=\frac{1}{5}\left[\right]\Rightarrow A B\left(A^{-1} B^{-1}\right)=\frac{1}{5}\left[\right] \neq 1. |A B|=0-5=-5\therefore(A B)^{-1}=\frac{-1}{5}\left[\right] \neq A^{-1} B^{-1}