The matrix $A$ in the image is given by:

$A = \begin{pmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{pmatrix}$

For part (i), which is asking to "Calculate the matrix", there could be further information needed (possibly determinant, inverse, etc.), but it is not clear in the current image. Could you provide additional parts of the question or clarify what you need specifically from matrix $A$?

Potential tasks related to this matrix could be:

1. Determining the determinant of the matrix $A$.
2. Finding the inverse of the matrix $A$ (if it exists).
3. Calculating the eigenvalues and eigenvectors.
4. Verifying if $A$ is orthogonal or symmetric.
5. Diagonalizing the matrix $A$, if possible.

Let me know which aspect you'd like to explore!

Tip: When working with square matrices, always check their determinant to determine properties like invertibility.