A　square　matrix　is　said　to　be　diagonalizable　if　it　is　similar　to　a　diagonal　matrix.　In　this　paper,　we　discuss　diagonability　of　matrices　over　commutative　semirings　and　give　an　equivalent　condition　for　an　idempotent　matrix　over　a　commutative　semiring　to　be　diagonalizable.　Also,　we　obtain　an　equivalent　description　for　a　matrix　over　a　multiplicatively　cancellative　and　commutative　semiring　to　be　diagonalizable.