Answer to Question #195791 in Linear Algebra for Rebecca

Question

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

Answer 1

Solution.

We have $n×n$ matrix, it is a square matrix. T will has inverse, if it must have full rank and this implies det T not equal 0.

And the rank of the matrix T is not full because it has

zero row. So, det T=0.

Therefore, T has no inverse.