The similarity transformations form the subgroup where A is a scalar times an orthogonal matrix.
From the en.wikipedia.org
The group of similarity transformations, i.e. affine transformations represented by a matrix A that is a scalar times an orthogonal matrix.
From the en.wikipedia.org
Assuming the pseudorange errors are uncorrelated and have the same variance, the covariance matrix on the right side can be expressed as a scalar times the identity matrix.