the matrix `[(0,1),(1,0)]` is the matrix reflection in the line

The matrix [(0,1),(1,0)] is the matrix of reflection in the line (A) x-y=0 (B) x+y=0 (C) x-y=1 (D) x+y=1

The matrix A= [[0,1],[1,0]] is

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y_(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of reflection about the line y=x .

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of reflection about the line y=x .

Consider point P(x, y) in first quadrant. Its reflection about x-axis is Q(x_(1), y_(1)) . So, x_(1)=x and y(1)=-y . This may be written as : {(x_(1)=1. x+0.y),(y_(1)=0. x+(-1)y):} This system of equations can be put in the matrix as : [(x_(1)),(y_(1))]=[(1,0),(0,-1)][(x),(y)] Here, matrix [(1,0),(0,-1)] is the matrix of reflection about x-axis. Then find the matrix of (i) reflection about y-axis (ii) reflection about the line y=x (iii) reflection about origin (iv) reflection about line y=(tan theta)x