Answer to Question #196882 in Linear Algebra for Regomoditswe Dibob

Question

Assume that T is an n × n matrix with a row of zeros. Prove that T has no inverse.

Answer 1

Inverse matrix:

$T^{-1}=\frac{T^T_*}{|T|}$

If a matrix T has a row of zeroes, the determinant of the matrix is 0.

Hence, T has no inverse.