Results that seem trivial, but are not

Question

I saw the Cayley-Hamilton theorem

Let $\mathbf{A}$ be a $n\times n$-matrix, and $p(\lambda)=\det(\lambda \mathbf{I}_n-\mathbf{A})$ the characteristic polynomial of $\mathbf{A}$. Then $p(\mathbf{A})=\mathbf{0}$

and I thought it was trivial since $\det(\mathbf{A}-\mathbf{A})=0$. I checked with Wikipedia and learned that this didn't work because $\lambda$ is a scalar, and $\det(\mathbf{0})$ is also a scalar, and not a matrix. This brings me to my question:

Are there any other results that seem trivial, but aren't?

Answer 1

The Jordan curve theorem states that, if you draw a closed non-intersecting curve in the plane, it divides the plane into those points that are inside the curve, outside it or on it.

Answer 2

The weak Goldbach conjecture (a theorem now, it seems, proved by Harald Helfgott): Every odd integer $n>5$ is a sum of three primes. If you try yourself examples, this seems trivially true. There are millions of possibilities for a big odd $n$. Nevertheless, the proof is extremely complicated.