Determinants Matrices Question 70
Question: If $ A= \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \\ \end{bmatrix} , $ then the value of $ |adjA| $ is
Options:
A) $ a^{27} $
B) $ a^{9} $
C) $ a^{6} $
D) $ a^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ Cofactormatrix= \begin{bmatrix} a^{2} & 0 & 0 \\ 0 & a^{2} & 0 \\ 0 & 0 & a^{2} \\ \end{bmatrix} $
$ \therefore $ adj A = (cofactor matrix) $ = \begin{bmatrix} a^{2} & 0 & 0 \\ 0 & a^{3} & 0 \\ 0 & 0 & a^{3} \\ \end{bmatrix} $ $ \therefore | adjA |= \begin{bmatrix} a^{2} & 0 & 0 \\ 0 & a^{2} & 0 \\ 0 & 0 & a^{2} \\ \end{bmatrix} =a^{6} $
BETA
