I have a rotation matrix represented by $$\left[ \begin{matrix} xx & xy & xz \\ yx & yy & yy \\ zx & zy & zz \\ \end{matrix} \right]$$ which is also an orthogonal matrix (determinant is +1). After reflecting about XY plane by using the matrix $$\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -1\\ \end{matrix} \right]$$ the determinant of the resultant matrix will be -1. What changes can I make to the resultant matrix so that the determinant becomes +1?
Below is an image for reference.enter image description here
I tried flipping one of the vectors, but that is changing the orientation of the part in CATIA. so it's a no go.
e.g. Matrix before reflection: $$\left[ \begin{matrix} 0.16 & 0 & 0.99 \\ 0 & 1 & 0 \\ -0.99 & 0 & 0.16\\ \end{matrix} \right]$$ Matrix after reflection about XY plane: $$\left[ \begin{matrix} 0.16 & 0 & -0.99 \\ 0 & -1 & 0 \\ -0.99 & 0 & -0.16\\ \end{matrix} \right]$$ Both matrices have determinant +1