Show that if A and B are row equivalent then they are equiva

Show that if A and B are row equivalent, then they are equivalent.

Solution

Sol. Since A and B are row equivalent then by definition B can be obtained from A by elementary row operations. Hence rank of A and B are equal .we know that two matrices are equivalent iff they have same rank. Since rank of A and B are same so A and B are equivalent. That is there exists non singular matrices P and Q such that B=P^-AP