Question

Let $A = \begin{bmatrix} 0 & 0 & - 1 \ 0 & - 1 & 0 \

• 1 & 0 & 0 \end{bmatrix}$, the only correct statement about the matrix A is

• A. $A^{2} = I$
• B. $A = ( - 1)I$, where I is unit matrix
• C. $A^{- 1}$does not exist
• D. A is zero matrix

Answer 1

Answer: (A)

$A^{2} = I$

Answer 2

$A^{2} = A.A = \begin{bmatrix} 0 & 0 & - 1 \ 0 & - 1 & 0 \

• 1 & 0 & 0 \end{bmatrix}\begin{bmatrix} 0 & 0 & - 1 \ 0 & - 1 & 0 \
• 1 & 0 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} = I$. Also,$A^{- 1}$exists as$|A| = 1$