Determinants Matrices Question 175
Question: If $ A= \begin{bmatrix} a & b \\ b & a \\ \end{bmatrix} $ and $ A^{2}= \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \\ \end{bmatrix} $ , then
Options:
A) $ \alpha =a^{2}+b^{2},\beta =ab $
B) $ \alpha =a^{2}+b^{2},\beta =2ab $
C) $ \alpha =a^{2}+b^{2},\beta =a^{2}-b^{2} $
D) $ \alpha =2ab,\beta =a^{2}+b^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ A^{2}= \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \\ \end{bmatrix} = \begin{bmatrix} a & b \\ b & a \\ \end{bmatrix} \begin{bmatrix} a & b \\ b & a \\ \end{bmatrix} $
$ = \begin{bmatrix} a^{2}+b^{2} & 2ab \\ 2ab & a^{2}+b^{2} \\ \end{bmatrix} $
$ \therefore \alpha =a^{2}+b^{2},\beta =2ab $
BETA
