Missing entry

The eigenvalues of a $2\times 2$ matrix fix both its trace and its determinant.

1. The trace equals the sum of the eigenvalues, so $3+b=1+6$ and $b=4$.
2. The determinant equals their product, so $3b-2a=1\times 6=6$.
3. With $b=4$ this reads $12-2a=6$, so $a=3$.

Answer: $3$