Let $A=\left(\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right)$. The only correct statement about the matrix $A$ is

(D) $\mathrm{A}=(-1) \mathrm{I}$, where I is a unit matrix

JEE Main · 2004 · 24 Apr 2004 · Offline · Matrices

Let

A = 00 - 1 0 - 1 0 - 1 00

. The only correct statement about the matrix

A

Answer: (B)

Just multiply

A

by itself. Because each row of

A

has a single non-zero entry, the product

A^{2}

comes out as the identity

I

. That one fact disposes of the other possibilities:

A

is plainly not the zero matrix, it is not

- I

since its diagonal entries are

0

, and from

A^{2} = I

we see

A

is its own inverse, so the inverse certainly exists. The correct description is

A^{2} = I

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option