Let $A$ be a $3 \times 2$ matrix with real entries. Let $H=A\left(A^T A\right)^{-1} A^T$ where $A^T$ is the transpose of $A$ and let $I$ be the identity matrix of order $3 \times 3$. Then

• A

  $H^2=I$
• B

  $H^2=-I$.
• Correct answer
  C

  $H^2=H$
• D

  $H^2=-H$

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