Good day to all.
We have just completed our chapter on matrix operations (matrix matrix product, special matrices etc...). In doing the end of chapter exercises I have across a problem where the following is asked:
Question: Find all 2x2 matrices where A^2 = 0
I considered the general 2x2 matrix A = [[a,b], [c,d]] where [a,b] and [c,d] are the rows of A.
Once I calculated AA I retrieved four equations which were the following:
(1) a^2 +bc = 0 => bc = -(a^2) => c= -(a^2) / b with b <> 0
(2) ab + bd = 0 => b(a+d) = 0 => b=0 or a = -d
(3) ac + dc = 0 => c(a+d) = 0 => c=0 or a = -d
(4) bc + d^2 = 0 => bc = -(d^2)
From here I assumed that a = -d and constructed the following matrix:
A = [[a,b],[(-a^2 / b), -a]] where the inner brackets represent the rows of A.
I was just wondering if the process used is correct? I apologize if the presentation leaves a lot to be desired. I am not sure of how to code matrices. Any help would be greatly appreciated.