Consider this matrix transformation: [[-1,0],[0,-1]] What is the geometric effect of this transformation? Choose 1 answer: A A reflection across the y axis B A reflection across the line y=x (c) A rotation about the origin by 90^(@) (D) A rotation about the origin by 180^(@)

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Consider this matrix transformation:  [[-1,0],[0,-1]] What is the geometric effect of this transformation? Choose 1 answer: A A reflection across the  y axis B A reflection across the line  y=x (c) A rotation about the origin by  90^(@) (D) A rotation about the origin by  180^(@)

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Identify matrix transformation: Identify the matrix transformation. The given matrix is: [[-1, 0],  [0, -1]]Effect on basis vectors: Understand the effect of the matrix on the basis vectors. The effect of the matrix on the basis vectors i (1,0) and j (0,1) will tell us the geometric transformation. Multiplying the matrix by i: [[-1, 0],  [0, -1]] * [1,               0] = [-1,     0]Effect on basis vector j: Understand the effect of the matrix on the basis vector j. Multiplying the matrix by j: [[-1, 0],  [0, -1]] * [0,               1] = [0,     -1]Analysis of transformation results: Analyze the results of the transformation on the basis vectors. The basis vector i (1,0) is transformed to (-1,0), and the basis vector j (0,1) is transformed to (0,-1). This means that the x-coordinate of any point is negated, and the y-coordinate of any point is also negated.Geometric effect of negating coordinates: Determine the geometric effect of negating both coordinates. Negating both the x and y coordinates of every point in the plane results in a reflection across the origin, which is equivalent to a rotation about the origin by 180 degrees.

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