How to solve for unknown variables in a matrix? 
How do I solve this problem? Ideally, I think $$a^2-4=1$$ is the best option to solve for a I set the entire expression equal to 1. Then to solve for b I just put $b=1$. Is this right? I feel like that's really wrong.
So update I got this

I suppose my answer is just b does not equal 0 and a does not equal +- sqrt 4

There's a fundamental result for this kind of problems:

A non-homogenous linear system $AX=B$ has solutions if & only if the matrix $A$ and the augmented matrix $A|B$ have the same rank. When this condition is satisfied, the common rank is the codimension of the affine subspace of solutions.

Therefore, if $(a^2-4)b\ne 0$, the matrix $A$ has rank $3$, which is also the maximum rank of  the augmented matrix, and there is a unique solution.
If $a=\pm 2$, $A$ has rank $2$, but the augmented matrix may have rank $3$. If it has rank $2$, the set of solutions has dimension $1$.
To determine the solutions, write the augmented matrix in reduced row echelon form. The set of solutions is the last column.
