It is a question from Mathematical Economics

1. Comment on the validity of the following statements (4 pts totally each): For each question, simply give answer for "True" or "False", and no explanation is needed. 1) The inverse of a matrix can exist if the matrix is not square. 2) Interchange two rows of a matrix; its rank will remain the same. 3) The rank of a matrix can exist if the matrix is not square. 4) If two matrices A*B=0, then it must be either A =0 or B =0. 5) The determinant of a matrix A, which is written as |A|, must be non-negative