Find two different 2 times 2 matrices A such that A^2=O .

Nannie Mack 2020-10-27 Answered
Find two different 2×2 matrices A such that A2=O .
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Expert Answer

bahaistag
Answered 2020-10-28 Author has 101 answers
Step 1
Let A=[abcd] be the 2×2 matrix.
Step 2
Then,
A2=[a2+bc(a+d)b(a+d)cd2+bc]
Given A0
So, find the values of a, b, c, d so that each element of A2=0
That is, when
a^2+bc=0
(a+d)b=0
(a+d)c=0
d^2+bc=0
so,
(a+d)b=0a+d=0a=d
adbc=0ad=bc
Step 3
For instance, put a=-d=1, b=-c=1 or put a=d=0, b=0, c=1. Then the matrices will be [1111],[0100]
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Jeffrey Jordon
Answered 2022-01-29 Author has 2047 answers

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