Determinants Matrices Question 135
Question: If $ A= \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \\ \end{bmatrix} $ and $ B= \begin{bmatrix} a^{2} & ab & ac \\ ab & b^{2} & bc \\ ac & bc & c^{2} \\ \end{bmatrix} $ , then AB is equal to
Options:
A) B
B) A
C) O
D) I
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ AB= \begin{bmatrix} 0 & c & -b \\ -c & 0 & a \\ b & -a & 0 \\ \end{bmatrix} \begin{bmatrix} a^{2} & ab & ac \\ ab & b^{2} & bc \\ ac & bc & c^{2} \\ \end{bmatrix} $
$ AB= \begin{bmatrix} abc-abc & b^{2}c-b^{2}c & bc^{2}-bc^{2} \\ -a^{2}c+a^{2}c & -abc+abc & -ac+ac \\ a^{2}b-a^{2}b & ab^{2}-ab^{2} & abc-abc \\ \end{bmatrix} $
$ = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{bmatrix} =O $
BETA
