Consider the matrix $A=\left[\begin{array}{ccc}1 & \sqrt{2} & 0 \\ \sqrt{2} & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$. Then, which of the following statements is/are true?
- All the eigenvalues of $A$ are real numbers
- The eigenvalues of $A^{-1}$ are $1, \dfrac{1}{2},-1$
- The determinant of $A$ is 3
- The matrix $A-2 I$ is invertible, where $I$ denotes the identity matrix of order $3 \times 3$
