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 $A\otimes A$ at each point $A\in GL(n,\mathbb{R})$

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

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

Edit: According to the comments on this question we clarify the identification $M_n(\mathbb{R})$ with $\mathbb{R}^{n^2}$: The identification is based on the lexicographic order on the index $i,j$ in $(a_{ij})$. For example $$ \begin{pmatrix} a_{11}&a_{12}\\ a_{21}&a_{22}\end{pmatrix}$$

is identified with $$(a_{11}, a_{12},a_{21}, a_{22})$$