Answer to Question #197273 in Linear Algebra for Snakho

Question

Show that if A is a matrix with a row of zeros (or a column of zeros) then A is not invertible

Answer 1

Matrix A is invertible then and only then when $det\,A \neq 0$.

One of the properties of determinants is that if a matrix has a row (column) with zeros then its determinant is zero. Therefore, if a matrix has a row (column) with zeros then $det \, A =0$ and it is not invertible.