MMN-1156
Multiplicative isomorphisms at invertible matrices
A. Armandnejad; M. Jamshidi;Abstract
Let $\mathbf{M}_n$ be the algebra of all $n \times n
$ matrices with entries in the field of real numbers.
For a matrix $Z\in \mathbf{M}_n$, it is said that a linear map
$T:\mathbf{M}_n\rightarrow\mathbf{M}_n$ is multiplicative at $Z$
if $T(AB)=T(A)T(B)$ whenever $AB=Z$. In this paper we investigate
some properties of multiplicative mapping at invertible matrices
and also we characterize all multiplicative isomorphisms at invertible matrices.
Then we give an example to show that multiplicativity at $I$ doesn't
imply multiplicativity on $\textbf{M}_n$, where $I\in\mathbf{M}_n$ is the identity matrix.
Vol. 15 (2014), No. 2, pp. 287-292