Answer
See proof below.
Work Step by Step
We know that
$1* A=1* [a_{ij}]=[1*a_{ij}]$
Since $a_{ij}]$ is a real number and $1$ is the identity number, then
$1* A=1* [a_{ij}]=[1*a_{ij}]=[a_{ij}]=A$
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