Question

Stan No
Let A = [ 1) which of the following matrices is zero?
O
A2
A2 + A + 51
O A2 - 3A + 51
O A -
50
A2 - A - 57
55
50​

Answer 1

Answer:

This is a proof question and I am not sure how to prove it. It is obviously true if you start with A=0 and square it.

I was thinking:

If A2=0

then AA=0

AAA−1=0A−1

IA=0

but the zero matrix is not invertible and that it was not among the given conditions.

Where's a good place to start?

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asked

Apr 15 '15 at 18:10

Alida

99●11 gold badge●11 silver badge●77 bronze badges edited

Jul 12 '17 at 17:02

Rodrigo de Azevedo

1

1

Hint: Nilpotent matrices. – Nigel Overmars Apr 15 '15 at 18:12

3

You were not given that A is invertible, so A−1 may not make sense. In fact, A2=0 proves it is not invertible, because the deteminant of A2 is the square of the determinant of A, so the determinant of A is zero. – Ross Millikan Apr 15 '15 at 18:22