Most important Linear Algebra theorems?

I was reading up on symmetric matrices and the textbook noted that the following is a remarkable theorem:

A matrix $A$ is orthogonally diagonalizable iff $A$ is a symmetric matrix.

This is because it is impossible to tell when a matrix is diagonalizable, or so it seems.

I haven’t gotten to realize yet how important this is, but I will soon. What, in your opinion , is the most important linear algebra theorem and why?

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