- #1

fluidistic

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## Homework Statement

Demonstrate that a matrix that has a null row is not invertible.

**2. The attempt at a solution**I know that saying that a matrix A is invertible is equivalent to say that A is row-equivalent and column-equivalent to the identity matrix.

And also that there exist elemental matrices E_1, E_2,...,E_r and F_1,...,F_s such that the identity matrix is equal to E_1...E_r A F_1...F_s.

So I could show that if A has at least a null row, then one of these properties cannot be true.

But still I don't know how to proceed. I understand clearly that if A has a null row, it's obvious that it cannot be equivalent to the identity matrix... but to prove it formally, I don't know how I can start. A little help is welcome.