Check which of the following matrices is positive definite and which is positive semi-definite:

Also, find the square root of the positive definite matrix.

To determine whether a matrix is positive definite or positive semi-definite, we need to check the eigenvalues of the matrix.

1. For a matrix to be positive definite, all of its eigenvalues must be positive.
2. For a matrix to be positive semi-definite, all of its eigenvalues must be non-negative.

Let's calculate the eigenvalues for both matrices A and B:

For matrix A:
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