Let $A$ be a $2 \times 2$ matrix with real entries such that zero is the only solution of the equation $\operatorname{det}(A-x \mathbf{I})=0$. Then

• Correct answer
  A

  $A^2=0$
• B

  $A=\mathbf{I}$
• C

  $A^2=A$
• D

  $A=0$

Hence, the correct answer is option: 'A'.