# Permutation matrix and invertible matrix

Proof: For every invertible matrix $$A$$ there is a permutation matrix $$P$$ and an invertible upper triangular matrix $$R$$ and $$R'$$, such that $$A=R'PR$$...

Can someone give me a hint? I dont even know where to start

• en.wikipedia.org/wiki/LU_decomposition Oct 18, 2021 at 11:46
• Are you sure you want A=R'PR Can you show me the excercise?
– Jam
Oct 18, 2021 at 12:47
• @Jam i am....i would show you but its in german....but i nearly translate word by word so should be correct Oct 18, 2021 at 13:04
• @Dmitry i know lu decomp....but does that apply`? Oct 18, 2021 at 13:04
• math.stackexchange.com/questions/758968/…
– Jam
Oct 18, 2021 at 13:17

Hint: If you matrix has as $$a_{11}$$ entry zero permute the row with a non zero row. Now start doing gauss ellimination. Keep all the accounting in matrix forms. Remember multiplying a matrix from the left gives sou row combinations as gauss ellimination does. Multiplying from right gives you collumn combinations. Can you do a similar method to get your result? (A is invertible so its not a zero matrix and a diagonal matrix is also an upper traingular) .