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Which of the following is (are) NOT the ...

Which of the following is (are) NOT the square of a `3xx3` matrix with real entries ?

A

`[(1,0,0),(0,1,0),(0,0,-1)]`

B

`[(1,0,0),(0,-1,0),(0,0,-1)]`

C

`[(-1,0,0),(0,-1,0),(0,0,-1)]`

D

`[(1,0,0),(0,1,0),(0,0,1)]`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`A=B^(2)implies |A|=|B|^(2)=`+ve
(1) `|(1,0,0),(0,1,0),(0,0,-1)|=1(-1) lt 0`
Matrix B can not possible.
(2) `|(1,0,0),(0,-1,0),(0,0,-1)|=1 (1-0) gt 0`
(3) `|(-1,0,0),(0,-1,0),(0,0,-1)|=-1 lt 0`
Matrix B can not be possible.
(4) `|(1,0,0),(0,1,0),(0,0,1)|=1 gt 0`
Matrix B can be `I` (identity matrix).
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