Simplify the Matrix [[0,-1],[-1,0]]

Problem

[[0,−1],[−1,0]]

Solution

1. Identify the given matrix. The matrix is a 2×2 square matrix with zeros on the main diagonal and −1 on the anti-diagonal.

2. Analyze the expression for potential simplification. In matrix algebra, "simplify" usually refers to performing arithmetic operations, reducing terms, or identifying a specific transformation matrix.

3. Determine if further operations are required. Since there are no scalar multipliers, additions, or multiplications with other matrices, the matrix is already in its simplest numerical form.

4. Recognize the matrix properties. This matrix represents a reflection across the line y=−x in a 2D Cartesian plane.

Final Answer

[[0,−1],[−1,0]]=[[0,−1],[−1,0]]

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