Is this a trivial counterexample to basic Rosen number theory exercise?

How to prove that when $n$ is even, and $A = (a_{ij})_{i,j}$, $1\leq i,j\leq n$ to show that $\mathrm{det} A = 1$?

If $\alpha=\sqrt[3]{2}$ and $p,q,r\in\mathbb{Q}$ then show $p+q\alpha+r\alpha^2$ is a subfield of $\mathbb{C}$

Translate this logical statement into natural language.

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Solve $\sin x + \cos x = \sin x \cos x.$

How to find the coefficients of an iteration of a polynomial function?

Is "taking a limit" a function? Is it a procedure? A ternary operation?

Why is $\det(I + A^{50}) = 4$ here?

Given a polynomial $P$ with integer coefficients, find $P(2)$

Why is $\sum_{p \in S_n} 2^{c(p)}$ equal to $(n+1)!$?

Weak lower semicontinuity of functional with two arguments

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