A is a 2x2 matrix. A^2=0; A is not equal to 0. What is A?

Question

*note: A^2 = A squared

Please do not merely cite the special characteristic of triangle matrices.

Please show your workings.

Answer 1

| . x . x |
| -x . -x |

where x is any real number and x ≠ 0 (The last part is only needed so that A will be non-zero). The transpose also works.

Multiply it out yourself. The result has nothing to do with triangular matrices, so I also suggest that you do not merely cite special characteristics of such matrices in your answer.

Answer 2

Let the matrix is
[a b
c d]
Then A^2 is
[a^2+bc b(a+d)
c(a+d) bc+d^2]
Equate each of these terms to zero ie
a^2+bc=0 b[a+d]=0 c[a+d]=0 bc+d^2=0
If u take [a+d] not equals zero then u get b=c=0 subsequently giving a=d=0 thus inadmissible
So a=-d and bc=-a^2
This can have many solns one being
a=1 d=-1 b=-1 c=1

Answer 3

Top-Left of A = x
Top-Right of A = -x
Bottom-Left of A = x
Bottom-Right of A = -x

I got your question to work for x=1 then I realized it could work for any x. The math I did was simple matrix multiplication. See my sources for how to do so.

Answer 4

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