Do the following Riemannian metrics on $GL(n,\mathbb{R})$ give us isometric structures?Do they generate the same volume forms? Is $O(n)$ a totally geodesic submanifold with respect to these metrics?

1. The metric with orthonormal frame $A\otimes A$ for $A\in GL(n,\mathbb{R})$

2. The metric with orthonormal frame $A\otimes A^{tr}$ $A\in GL(n,\mathbb{R})$

Note that the tangent space at each point $A$ is identified with $M_{n^2}(\mathbb{R})$.