In this paper, we derive Ostrowski and Brauer type theorems for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. After that, a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds is derived for the zeros of quaternionic polynomials.