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## Homework Statement

I was doing this practice exam and I had to calculate the eigenvalues en vectors. The matrix had two eigenvalues, I calculated one eigenvector. But when I was performing row operations for the second eigenvector, the matrix with the second eigenvalue substitued became an identity matrix, which kinda blew my mind.

So my question is what does this mean? Does it mean that the matrix doesn't have any eigenvectors? And is it possible that it can become an identity matrix? Also I'm pretty sure that I didn't make a mistake, I put the matrix on my calculator and used the funcion "Rref" on it and the result was the identity matrix. Any help would be appreciated!