Determinants Matrices Question 11
Question: If A is an orthogonal matrix of order 3 and $ B= \begin{bmatrix} 1 & 2 & 3 \\ -3 & 0 & 2 \\ 2 & 5 & 0 \\ \end{bmatrix} , $ then which of the following is/are correct- 1. $ |AB|=\pm 47 $ 2. $ AB=BA $ Select the correct answer using the code given below:
Options:
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] The determinant of a orthogonal matrix is always $ \pm 1 $
$ |A|=\pm 1 $
$ B= \begin{bmatrix} 1 & 2 & 3 \\ -3 & 0 & 2 \\ 2 & 5 & 0 \\ \end{bmatrix} $
$ |B|=-10-2(-4)+3(-15) $
$ =-47 $
$ |AB|=|A||B| $
$ =(\pm 1)(-47) $
$ =\pm 47 $ Taking A as identity matrix we can prove $ AB=BA $
BETA
