Coordinate system A : with Origin at (0, 0, 0), x-axis = (1, 0, 0), y-axis=(0,1,0), z-axis=(0,0,1) Coordinate system B: with origin at (1, 1, 1), x-axis= (-1, 0, 0), y-axis=(0,0,-1), z-axis=(0,-1,0)

I want to change B to A by aligning the center and the axis. So I tried Multiplying by Transformation Matrix M which consists of Rotation (Rotate the Z-axis by 90 degrees) and Translation matrix (to translate origin ). But my rotation matrix is wrong . This is my rotation matrix: R= cos(90) -sin(90) 0 sin(90) cos(90) 0 0 0 1

which yields: (0 -1 0) 1st row (1 0 0) 2nd row (0 0 1) 3rd row But this matrix is wrong since it doesn’t rotate the axis of B to align with A. The correct rotation materix is ( -1 0 0) 1st row (0 0 -1 ) 2nd row (0 -1 0) 3rd row

But I dont understand how could this matrix make the correct rotation. Coordinates A and B as I see them