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PCA in the exam 2019

Could someone help to explain to me why this statement is wrong?
In PCA, the first principal direction is the eigenvector of the data matrix X with the largest associated eigenvalue.
Thanks in advance.

The eigenvectors are of the covariance matrix XX.T or X.TX, not X alone.

I think this is correct:
In PCA, the first principal direction is the eigenvector of the data matrix XX.T with the largest associated eigenvalue.

It's actually the singular values, not eigenvalues.

I think both singular values and eigenvalues are correct, since eigenvalues of matrix XX.T are squared singular values of data matrix X.

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