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Could someone help with a proof: $F^*$ $I_n$ is normal in $GL_n(F)$.


Notice GL maps to F*:

$det:GL_n(F) \mapsto F^*$ by the determinant map.

And notice it maps back:

$F^* \mapsto GL_n(F)$ by ($a \mapsto aI_n$) where $a \epsilon F^*$

Also note:

Not dot product (so $F^*I_n$ is not a scalar vector, it is a diagonal matrix)

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