Where n is the number of columns of matrix A and the number of rows of matrix B. This formula has important applications in matrix theory and linear algebra. This formula can be obtained through a series of mathematical derivation. First of all, we know that the rank of a matrix represents the maximum number of linearly independent columns or rows in the matrix. When two matrices A and B are multiplied to get a new matrix ab, the rank (rab) of AB represents the maximum number of linearly independent columns or rows in AB. According to the definition of matrix multiplication, the rank rab of ab will not exceed the sum of rank ra of matrix A and rank rb of matrix B, because the columns or rows in AB are composed of A and B, and the number of linearly independent columns or rows in A and B will not increase. However, because the number of columns of AB is limited by the number of columns of matrix A and the number of rows of matrix B, we need to subtract n, that is, the number of columns of matrix A and the number of rows of matrix B, to ensure that the actual number of columns or rows of AB is not exceeded. Therefore, rab ≥ ra+rb-n is an important matrix rank inequality, which is widely used in matrix theory and linear algebra.