Question

How would I explain that if A is an nxn matrix then it is equivalent to saying that reduce row echelon form of A is In?

Answer 1

I sub n not ln

Answer 2

And I don't see how that is equivalent b/c can't you have a row that's all 0's

Answer 3

you can have a row that is all 0's, so i am also confused by this statement.

Answer 4

you cant assume that A is equivalent to the identity matrix. Are there any conditions on A? like having a non-zero determinant or something like that.

Answer 5

It's in my textbook it says, If A is an nxn matrix then the following statements are equivalent: then the first one says reduced row echelon form of A is I sub n then the next says A is invertible

Answer 6

There we go, yes that is true. if you can row reduce A to the identity matrix, then A is invertible, and if A is invertible, that means if can be reduced to the identity matrix.

Answer 7

Oh I see what you mean, that make sense thanks!