MATH0007 video 24 - invertibility and RREF
A square RREF matrix which is not equal to the identity has a column with no leading entry. If E is invertible, EA is invertible if and only if A is invertible. A matrix is invertible if and only if there is a sequence of row operations taking A to the identity matrix. A matrix A is invertible if and only if the only solution to Ax = 0 is the zero vector.