Determinants Matrices Question 104
Question: The matrix $ A= \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} $ is
Options:
A) Idempotent matrix
B) Involutory matrix
C) Nilpotent matrix
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ A^{2}= \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} \begin{bmatrix} -5 & -8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & -1 \\ \end{bmatrix} $
$ = \begin{bmatrix} 25-24+0 & 40-40+0 & 0+0+0 \\ -15+15+0 & -24+25+0 & 0+0+0 \\ -5+6-1 & -8+10-2 & 0+0+1 \\ \end{bmatrix} $
$ = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} =I $ Hence, the matrix A is involutory.
BETA
