Question

If A = $\begin{bmatrix} 2 & - 2 & - 4 \

• 1 & 3 & 4 \ 1 & - 2 & x \end{bmatrix}$ is an idempotent matrix then x =

• A. -5
• B. -1
• C. -3
• D. -4

Answer 1

Answer: (C)

-3

Answer 2

Here $A^{2} = A$

⇒$\begin{bmatrix} 2 & - 2 & - 16 - 4x \

• 1 & 3 & 16 + 4x \ 4 + x & - 8 - 2x & - 12 + x^{2} \end{bmatrix} = \begin{bmatrix} 2 & - 2 & - 4 \
• 1 & 3 & 4 \ 1 & - 2 & x \end{bmatrix}$On comparing$16 + 4x = 4 \Rightarrow x = - 3$