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## Homework Statement

Prove that is ##A## is lower triangular and ##B_{ij}## is the matrix that results when the ith row and jth column of A are deleted, then ##B_{ij}## is lower triangular if i > j.

## Homework Equations

## The Attempt at a Solution

I know that a square matrix is lower triangular if and only if the jth column starts with at least j-1 zero's for every j.

I am attemting to prove this by contradiction.

If i = j, then the jth column of B has j-1 zeros, but this is true?

if i was to take a 4 x 4 lower triangluar matrix and delete its first row and first column would the 1st,2nd,3rd,4th columns have 0,1,2,3 zeros respecively?

Lets ignore that, prehaps I am saying/doing something silly, to finish my proof by contradiction i also have to show that for i < j, we don't have a lower triangular matrix.

if the ith row and the (i+n)th collumn, where n is a postitive integer, of A is deleted, then the ...

ah I am really not getting this one guys. I am lost.