NDA 2023
- Exam
- NDA
- Year
- 2023
- Subject
- Mathematics
- Chapter
- Matrices
NDA 2023 · Mathematics · Matrices
If A=[ array ccc 0 & 3 & 4 -3 & 0 & 5 -4 & -5 & 0 array ] , then...
If A=\left[\right], then which one of the following statements is correct?
Options
- A\mathrm{A}^2\operatorname\det\left(\mathrm{A}^2\right)=0
- B is symmetric matrix with
- C\mathrm{A}^2\operatorname\det\left(\mathrm{A}^2\right)=0
- D is skew-symmetric matrix with
Correct answer
A. \mathrm{A}^2\operatorname\det\left(\mathrm{A}^2\right)=0
Step-by-step solution
Since the matrix A is skew symmetric of order 3 (odd)
So, |A|=0 and is symmetric matrix
Now
Similarly,
Hence \left|4 \mathrm{~A}^4\right|-\left|3 \mathrm{~A}^3\right|+\left|2 \mathrm{~A}^2\right|-|\mathrm{A}|+(-1)^3\left|\mathrm{I}_3\right|=-1