By using the properties of that all the elements in each row of rank-1 matrix are proportional, matrix elementary transformations and determinants, the claw-decomposition of rank-1 square matrix, eigenpolynomial, the eigenvalues of AAT, inequalities of trA and tr(AAT) are discussed. Also, some responding results about μA + vE are generalized to μA + vQ, and several applications of some properties of rank-1 square matrix are given.