A mistake in a linear equation system led us to explore the relationship between the existence of matrix B,such that BA=I,and the unique solution of the linear equation system AX=b,where A is an arbitrary matrix and I is an identity matrix.Furthermore,for any matrix A we find sufficient and necessary condition for the existence and uniqueness of B,such that BA=I.And if matrix B exists,we construct B.We also point out the sufficient and necessary condition under which BA=I and AB=I can occur simultaneously.
linear equationssolutionsetmatrix multiplicationidentity matrixrank
万方数据
维普
