Let `{:A=[(0,0,-1),(0,-1,0),(-1,0,0)]:}`. The only correct statement aboul the matrix A is

Options

A. A is a zero matrix
B. `A=(-1)l` where `l` is a unit matrix
C. `A^(-1)` does not exist
D. `A^(2)=l`

Answer

D

Explanation

a. It is clear that, A is not a zero matrix.
b. `(-1)l=-1[(1,0,0),(0,1,0),(0,0,1)]=[(-1,0,0),(0,-1,0),(0,0,-1)]!=A`
i.e. `(-1)l!=A`
c. `|A|=0|(-1,0),(0,0)|-0|(0,0),(-1,0)|-1|(0,-1),(-1,0)|`
`=0-0-1(-1)=1!=0`
Since `|A|!=0`. So `A^(-1)` exists.
d. `A^(2)=[(0,0,-1),(0,-1,0),(-1,0,0)][(0,0,-1),(0,-1,0),(-1,0,0)]`
`impliesA^(2)=[(1,0,0),(0,1,0),(0,0,1)]impliesA^(2)=l`