Let `A=[(0,0,-1),(0,-1,0),(-1,0,0)]` Then only correct statement about the matrix A is (A) A is a zero matrix (B) `A^2=1` (C) `A^-1` does not exist (D) `A=(-1)` I where I is a unit matrix

Options

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

Answer

D

Explanation

We have, `absA=1 ne 0`.
So, `A^(-1)` exists.
Clearly, `A ne (-1)I and A` is not a zero or null matrix.
options (a),(b) and (c ) are not correct.
Now, `{:A^2=[(0,0,-1),(0,-1,0),(-1,0,0)][(0,0,-1),(0,-1,0),(-1,0,0)]=[(1,0,0),(0,1,0),(0,0,1)]=I:}`
Hence, option (d) is correct.