If you add a row of A to another row, or exchange rows, the eigenvalues
usually change. Elimination does not preserve the Eigen values.
A better way is to check if | A- λI| = 0, If 1 (given in the question) is the eigen value of this matrix. and the charactersitic equation satisfies. By doing so for all the matrix we find the equation satisfies for first matrix.
Hence the answer is one , ie, option A
I found this way much faster then finding the values and then checking if the eigen values.