https://file.aiquickdraw.com/mathbot/file/17270153402100gy3j8to.jpg

The matrix \( A \) in the image is given by:

\[
A = \begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix}
\]

Part (i) of the question asks you to calculate the matrix \( A^2 \), which is the square of the matrix \( A \).

Let’s begin by calculating \( A^2 \). The general formula for squaring a matrix is multiplying the matrix by itself:

\[
A^2 = A \times A
\]

Given the matrix:

\[
A = \begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix}
\]

Let me now calculate \( A^2 \).The square of the matrix \( A \) is:

\[
A^2 = \begin{bmatrix} -2 & 3.464 \\ -3.464 & -2 \end{bmatrix}
\]

Would you like a further breakdown of this calculation or any additional details?

Here are five related questions you might want to explore:
1. What are the eigenvalues and eigenvectors of matrix \( A \)?
2. Can you calculate the determinant of matrix \( A \)?
3. What is the trace of matrix \( A \)?
4. How do you compute the inverse of matrix \( A \), if it exists?
5. Is matrix \( A \) orthogonal?

**Tip:** When multiplying matrices, remember that matrix multiplication is not commutative, meaning \( A \times B \neq B \times A \) in general.

The matrix A is defined by A = [[-1, -sqrt(3)], [sqrt(3), -1]]. Calculate the matrix A^2.

Learn how to calculate the square of matrix A, defined as A = [[-1, -sqrt(3)], [sqrt(3), -1]], using matrix multiplication. This example covers key linear algebra concepts, including matrix exponentiation and multiplication. Suitable for advanced high school or undergraduate students.

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