fast inverse

static Float4x4 Inverse(const Float4x4& matrix)
{
    Float4x4 out(Float4(0.0));
    // Inverse of the 3x3 rotation matrix is just its transpose
    out.x.x = matrix.x.x;
    out.x.y = matrix.y.x;
    out.x.z = matrix.z.x;
    // -- //
    out.y.x = matrix.x.y;
    out.y.y = matrix.y.y;
    out.y.z = matrix.z.y;
    // -- //
    out.z.x = matrix.x.z;
    out.z.y = matrix.y.z;
    out.z.z = matrix.z.z;
    // Inverse of the translation vector is Multiply(-translationVector, Transpose(rotationMatrix));
    Float3 negativePosition = -Float3(matrix.x.w, matrix.y.w, matrix.z.w);
    // -- //
    out.x.w = Dot(negativePosition, out.x.xyz);
    out.y.w = Dot(negativePosition, out.y.xyz);
    out.z.w = Dot(negativePosition, out.z.xyz);
    // .w.w should be 1.0 :p
    out.w.w = 1.0;

    return out;
}