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Let A be any matrix such that A2=0 matrix then does it implies A is a zero matrix?

Let A be any matrix such that A2=0 matrix then does it implies A is a zero matrix?

Grade:12

3 Answers

prashanth
22 Points
9 years ago

yes

Vinay Modani
22 Points
9 years ago

Not necessarily. 

If A2 = 0, then such matrix A is known as Nilpotent Matrix. 

e.g. A = 

0 1
0 0

This matrix A is not equal to zero but A2 will be equal to zero. 

Amit Jain
askIITians Faculty 32 Points
9 years ago
Not at all. Consider A = 0 1
0 0
It is not zero but A^2=0.

Amit Jain
IITD
AskIITians

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