Given Trace of powers of A, how to find its determinant Hello everyone,
              I am given trace of $A$, $A^2$, and $A^3$, how do I find determinant of $A$ from this. $A$ is $3\times 3$ matrix. Can this be solved using norm ?
Thanks in advance.

Let $\lambda_i$ be eigenvalues of $A$. Use relations between trace and eigenvalues like
$$
Tr(A)=\lambda_1+\lambda_2+\lambda_3
$$
$$
Tr(A^2)=\lambda_1^2+\lambda_2^2+\lambda_3^2
$$
$$
Tr(A^3)=\lambda_1^3+\lambda_2^3+\lambda_3^3
$$
Solve above to get $\lambda_i$ and
$$
\det(A)=\lambda_1\lambda_2\lambda_3
$$
You can see this method can easily be extended to $n\times n$ matrix.
