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Sample rate conversion systems (expansion or decimation) are time-varying operators.
For your example system of decimation by $M$ :
$$ y[n] = T\{x[n]\} = x[Mn] $$
you can easily see that results of shift in the input and output are not the same; i.e.,
$$ y_1[n] = T\{ x[n-d] \} = x[Mn - d] $$
and
$$ y_d[n] = y[n-d] = x[M(n - d)] \neq y_1[n]$$
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