1. The problem statement, all variables and given/known data Prove or disprove the following statement: If A is a singular matrix (detA=0) the it's similar to a matrix with a row of zeros. 2. Relevant equations 3. The attempt at a solution I know that A has an e-value 0 which means that it's similar to a matrix that has a column of zeros but how do I relate that to the rows? Thanks.
Since det(A)=0, there is a row relation. Or, consider what you do know. A^t has det 0, so there is an M with (MA^tM^-1) a matrix with a column of zeroes. Now how do we get A back out again?