Consider the linear transformation, , for which is found by first rotating the point through an angle of anticlockwise about the origin and then reflecting that point across the line .

Find the 2x2 matrix A for which

I understand how to transform matrices in the required ways described above, what I don't understand is which matrix I am transforming to begin with, i.e., to rotate a matrix anticlockwise bt \frac{\pi}{3} I just multiply it by:

Similarly, to reflect a matrix across the line y = x I just multiply it by:

What I don't understand in this question is which matrix I am transforming in the first place? What does rotating the point x mean? What matrix am I transforming by multiplying it by:

Which matrix is A and which is x? do I need to multiply everything by the column vector or something?

Thanks.