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

Options

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)]`

Answer

A, C

Explanation

`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).