The correct answer is $\boxed{\text{D}}$.
An eigenvalue of a square matrix $M$ is a number $\lambda$ such that there exists a nonzero vector $v$ such that $Mv=\lambda v$. In other words, an eigenvalue is a number that $M$ maps to itself when multiplied by a nonzero vector.
If the entries in each column of a square matrix $M$ add up to 1, then $M$ is a stochastic matrix. A stochastic matrix is a matrix with non-negative entries such that the sum of the entries in each row is 1.
It can be shown that any stochastic matrix has at least one eigenvalue equal to 1. This is because the vector $v$ with all entries equal to 1 is a solution to the equation $Mv=\lambda v$ for any $\lambda$.
Therefore, if the entries in each column of a square matrix $M$ add up to 1, then an eigenvalue of $M$ is $\boxed{\text{1}}$.
Here is a more detailed explanation of each option:
- Option A: $4$. This is not an eigenvalue of any square matrix. A square matrix has $n^2$ eigenvalues, where $n$ is the number of rows and columns in the matrix. The eigenvalues of a square matrix are always real numbers. The sum of the eigenvalues of a square matrix is equal to the trace of the matrix, which is the sum of the elements on the main diagonal of the matrix. The product of the eigenvalues of a square matrix is equal to the determinant of the matrix.
- Option B: $3$. This is not an eigenvalue of any square matrix. A square matrix has $n^2$ eigenvalues, where $n$ is the number of rows and columns in the matrix. The eigenvalues of a square matrix are always real numbers. The sum of the eigenvalues of a square matrix is equal to the trace of the matrix, which is the sum of the elements on the main diagonal of the matrix. The product of the eigenvalues of a square matrix is equal to the determinant of the matrix.
- Option C: $2$. This is not an eigenvalue of any square matrix. A square matrix has $n^2$ eigenvalues, where $n$ is the number of rows and columns in the matrix. The eigenvalues of a square matrix are always real numbers. The sum of the eigenvalues of a square matrix is equal to the trace of the matrix, which is the sum of the elements on the main diagonal of the matrix. The product of the eigenvalues of a square matrix is equal to the determinant of the matrix.
- Option D: $1$. This is an eigenvalue of any stochastic matrix. A stochastic matrix is a matrix with non-negative entries such that the sum of the entries in each row is 1. It can be shown that any stochastic matrix has at least one eigenvalue equal to 1. This is because the vector $v$ with all entries equal to 1 is a solution to the equation $Mv=\lambda v$ for any $\lambda$.