matrix function onto and 1-1 I have just started a linear algebra paper and we are doing 1-1 and onto functions. I understand in theory what they mean, I just don't know how to prove them.
For example: 
Define $f: M_2(\mathbb{R}) \to \mathbb{R} \text{ by } f(\begin{bmatrix}a&b\\c&d \end{bmatrix})=b$
Show that this is onto (or not) and 1-1 (or not)
**Edit**
So I'm a bit confused about what it means for $f(\begin{bmatrix}a&b\\c&d \end{bmatrix})=b$. How does a matrix equal a single value?
 A: Hints (straight from the definitions):
Consider any arbitrary $x \in \mathbb{R}$.  Are we guaranteed a matrix $M$ such that $f(M) = x?$  If so, then $f$ is onto.
Next, let's say $f(M) = x$ for some $x \in \mathbb{R}$.  Is $M$ the only matrix such that $f(M) = x$?  If so, then $f$ is one-to-one.

Edit to respond to OP edit:
The function is taking matrices and mapping them to constants.  It's perfectly valid.  Go back to your original definition of a function.  A function is a relation between two sets: inputs and outputs such that each input has a unique output.  As far as the inputs and output sets are concerned -- they can be anything.  Here, the inputs are a set of matrices, and the outputs are a set of numbers, namely the real numbers.  
Note that this is a function because, for any given matrix, you are going to get a unique output.  Now, perhaps it's not a very useful function, and that's kind of the point.  It's simply an exercise to check your understanding of one-to-one/onto in a slightly more abstract setting.
