Determinants Matrices Question 140
Question: If $ A= \begin{bmatrix} 0 & 1 \\ 0 & 0 \\ \end{bmatrix} $ , I is the unit matrix of order 2 and a, b are arbitrary constants, then $ {{(aI+bA)}^{2}} $ is equal to
Options:
A) $ a^{2}I+abA $
B) $ a^{2}I+2abA $
C) $ a^{2}I+b^{2}A $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{(aI+bA)}^{2}}=a^{2}I^{2}+b^{2}A^{2}+2abAI $
$ =a^{2}I^{2}+b^{2}A^{2}+2abA $ But $ A^{2}= \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ \end{bmatrix} \therefore {{(aI+bA)}^{2}}=a^{2}I+2abA $ .
BETA
