question_answer

Let\[A=\left[ \begin{matrix}    0 & 0 & -1  \\    0 & -1 & 0  \\    -1 & 0 & 0  \\ \end{matrix} \right].\]The only correct statement about the matrix A is

A) A is a zero matrix

B) \[A=(-\text{ }1)l,\]where\[l\]is a unit matrix

C) \[{{A}^{-1}}\]does not exist

D) \[{{A}^{2}}=l\]

Correct Answer: D

Solution :

Given matrix (a) It is clear that A is not a zero matrix. (b)                 (c) Since, . So,exists. (d)