Question

Let it be the matrix A, with the property:

Answer 1

matrix A: \[\left(\begin{matrix}a & b \\ c & d\end{matrix}\right)\]

Answer 2

its property: \[A^{2} = O_{2}\]

Answer 3

solve the equation: \[X^{2} = A\] for a = 1

Answer 4

\[A^{2} = \left(\begin{matrix}1+bc & b(d+1) \\ c(d+1) & bc+d^{2}\end{matrix}\right)\]

Answer 5

after solving the equation system i get : \[A = \left(\begin{matrix}1 & \frac{ -1 }{ c } \\ c & -1\end{matrix}\right)\]

Answer 6

the Trace is 0, same as the determinant.

Answer 7

what is \(O_2\) ?

Answer 8

\[\left(\begin{matrix}0 & 0 \\ 0 & 0\end{matrix}\right)\]

Answer 9

so what'st the question?

Answer 10

i have to solve the equation : \[X^{2} = \left(\begin{matrix}a & b \\ c & d\end{matrix}\right) \] for a = 1