Prove/Disprove: Similar Matricies w/ Zero Rows

[daniel_i_l]

Homework Statement

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.

Homework Equations

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.

 

[mjsd]

ok, note that det (M) = product of eigenvalues of M

 

[matt grime]

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?