Answer to Question #193074 in Linear Algebra for prince

Question

Show that if A is a matrix with a row of zeros (or a column of zeros), then A cannot have an inverse

Answer 1

f a matrix has a row of zeroes or a column of zeros, the determinant of the matrix is 0. (You calculate the determinant of the matrix by choosing a row or column and multiplying each element of it with the adjoint of the smaller matrix obtained after removing the respective row and column. When each element is zero, the total determinant is also zero. )

If determinant is zero, $A^{-1} =$ $adj(A)\over det(A)$ $A$ is not defined. So, A is not  invertible.