Based on existing knowledge about Kronecker product of two matrices and matrix operations such as multiplying two matrices, computing the determinant of a square matrix and finding the inverse of a square matrix, the article clarifies the concept of Kronecker product of two matrices and some of its properties are related to matrix operations known above. The article will also present the application of Kronecker product in large-order matrix operations such as multiplying two matrices, computing the determinant of a square matrix and finding the inverse of a square matrix with specific illustrative examples. Applying Kronecker product in those matrix operations known above will significantly reduce the amount of calculation.