Do the following Riemannian metrics on $GL(n,\mathbb{R})$ give us isometric structures?

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 $M_{n^2}(\mathbb{R})$.