Question

let A be a nonsingular matrix. Prove that if B is row-equivalent to A then B is also non singular

Answer 1

If B is row equivalent to A then by row operation we can turn B into A. But A is non singular. So by ro operations we can turn A to I. Therefore we can turn B into I by some row operations. Which means that B is non singular as well

Answer 2

Thanks that was awesome lOL