Absolute value of the determinant of a linear map between two equal dimensional Euclidean vector spaces is independent of orthonormal basis

Question

Let $V_1$ and $V_2$ be two Euclidean vector spaces with the same dimension, and let $f : V_1 \longrightarrow V_2$ be a linear map between them. If $M$ is the matrix of the map $f$ relative to two orthonormal bases of $V_1$ and $V_2$.

Prove that the $|det M|$ does not depend on the bases chosen.

Let $A$ be the matrix of linear map with respect to the old basis $B$ and $C$ of $V_1$ and $V_2$ respectively.

Let $A^{\prime}$ be the matrix of linear map with respect to the new basis $B^{\prime}$ and $C^{\prime}$ of $V_1$ and $V_2$ respectively.

Then, $B^{\prime}=BP$ ,$C^{\prime}=CQ$ and $A^{\prime}=Q^{-1}AP$

Now I am stuck here how to connect the idea of orthonormal basis to this and prove.