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This is the last followup question to my other question. Here I have a matrix $M$ whose kernel is the field $\mathbb{F_p}$. I'm not sure what this expression is saying or why it is important. My understanding is that $\mathbb{F_p}$ is a field that contains individual non-vector elements so how can this possibly be in the kernel of matrix $M$?

For example, let us say that I have this matrix in $\mathbb{F_3}$ when is that matrix's kernel $\mathbb{F_3}$ ?

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    To reiterate the previous comment, $\Bbb{F}_3$ is the 1-dimensional vector space over itself. Any matrix over a field $K$ has $K$ for its kernel whenever it has a $1$-dimensional kernel.2012-10-27
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    @DevenWare Please consider converting your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-08-22

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