Final answer:
To find the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0), we need to first find the reflection matrix and then multiply it by the rotation matrix. The matrix that represents the combined transformation is M = [-1 0; 0 -1].
Step-by-step explanation:
To find the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0), we need to first find the reflection matrix and then multiply it by the rotation matrix.
The reflection in the line y=x can be represented by the matrix R = [0 1; 1 0].
The rotation by 90° anticlockwise about (0,0) can be represented by the matrix C = [0 -1; 1 0].
To find the matrix that represents the combined transformation, we multiply R and C: M = R * C = [0 1; 1 0] * [0 -1; 1 0] = [-1 0; 0 -1].
Therefore, the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0) is M = [-1 0; 0 -1].