Inverting all values in matrix Lets say I have a matrix:
$$\left[\begin{array}{cc}
    2 & 4 \\
    3 & 7 \\
\end{array}\right]
$$
And my maximum range value is $10$, how would I go about creating another matrix that inverts those values? So that the matrix would end up looking like:
$$\left[\begin{array}{cc}
    8 & 6 \\
    7 & 3 \\
\end{array}\right]
$$
In algebraic form?
 A: Based on your example, it looks like you're asking the following:

Given $m>0$, is there some way to transform $$\left[\begin{array}{cc}a & b\\c & d\end{array}\right]\mapsto\left[\begin{array}{cc}m-a & m-b\\m-c & m-d\end{array}\right]$$ for all $a,b,c,d$ between $0$ and $m$ (inclusive)?

The answer to that question is: "Yes, but it isn't necessarily very interesting." Let $J$ be the $2\times 2$ matrix of $1$s. Then for any $m>0$ and any $2\times 2$ matrix $A$ with entries between $0$ and $m$ (inclusive), the matrix $m\cdot J-A$ does the trick (where $m\cdot J$ indicates scalar multiplication by $m$).
If that's not what you were trying to ask, then please clarify. It might help if you told us what led you to ask this question, too.
A: Look at the individual entries in the matrix, and see what relationship you can find between those entries, and the "maximum range value".
From your example, in the $(1,1)$ cell in the first matrix, you have the entry $2$.  In the second matrix, you have the entry $8$. Your maximum value is $10$.  Can you see some relationship between the numbers $2$, $8$, and $10$?  Does this relationship hold for the other values? (for example, $3$, $7$, and $10$)
Leave a comment if you need more guidance.  (I'm experimenting with my answering style from just giving an answer to trying a more Socratic method... so I'm looking for feedback.)
