# Row space of a matrix?

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• Sep 28th 2009, 02:36 PM
altave86
Row space of a matrix?
How do I prove:

$row(A^2)\subset row(A)$, for a matrix A
• Sep 29th 2009, 07:49 AM
aman_cc
each row of A^2 can be shown to be linear combination of rows of A. (look at the definition of matrix multiplication). Hence row space of A^2 is a subset of row space of A.

Not sure if there is another more conceptual argument.
Thanks