In 3D, rotation matrices are used to rotate objects around the x, y, or z axes. Each axis has its own specific rotation matrix. For example, rotating around the z-axis uses a matrix that leaves the z-coordinate unchanged but rotates the x and y coordinates, effectively spinning the object in the xy-plane. Similarly, rotating around the x-axis affects the y and z values, while rotating around the y-axis affects the x and z values. These 3x3 matrices are always orthogonal, meaning their rows and c

In 3D transformations, dilation and rotation matrices serve distinct but complementary roles. A dilation matrix uniformly scales a vector in all directions by a constant factor, effectively expanding or contracting the object while preserving its shape and orientation—this is represented by multiplying the identity matrix by the scalar factor. In contrast, a rotation matrix in 3D rotates points around a fixed axis (typically x, y, or z) while preserving distances and angles. These rotation matri