What is the effect of rotations to the signs in a matrix?

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I'm not very knowledgeable in math, so please forgive me for any mistakes I make in my explanation of my issue. I am writing a script in a 3D application that mirrors these Matrices to the other side of the ZY global axis. The thing I care about is what is being negated as the object's axis is rotated.

In order to understand the math behind this, I am using a script that rotates the x-axis of an object in 90 degrees three times.

rotX 0: Matrix(v1: (0.975, 0.171, -0.141); v2: (-0.141, 0.97, 0.199); v3: (0.171, -0.174, 0.97); off: (210, 10, 10))
rotX 90: Matrix(v1: (0.975, 0.171, -0.141); v2: (-0.171, 0.174, -0.97); v3: (-0.141, 0.97, 0.199); off: (210, 10, 10))
rotX 180: Matrix(v1: (0.975, 0.171, -0.141); v2: (0.141, -0.97, -0.199); v3: (-0.171, 0.174, -0.97); off: (210, 10, 10))
rotX 270: Matrix(v1: (0.975, 0.171, -0.141); v2: (0.171, -0.174, 0.97); v3: (0.141, -0.97, -0.199); off: (210, 10, 10))
  • I can see that the first 90° rotation is negating the v2.z, v3.x, and v3.y.
  • The second 90° rotation, 180°, is negating the v2.x, v2.y, v3.x, and v3.z.
  • The third 90° rotation, 270°, is negating the v2.z, v3.x, and v3.y.

Looking at these values, I cannot understand the pattern. I think that, because I am rotating in the X axis, that is the reason the v1 Vector representing the x-axis is unaffected. The object isn't changing position so that is why off, the position vector, is not affected.

In order to write a function that will know which values to negate for each 90° rotation, I need to understand the math behind it, which is why I am here.

Can any kind souls out there please help me understand this or help me point me in a direction towards solving this problem?

Thank you!