Determinant of a block skew-symmetric matrix

By diagonalization in the $2\times 2$ case, we obtain the similarity relation $$ \pmatrix{A&-B\\B&A}=\pmatrix{-iI&iI\\I&I}\pmatrix{A-iB&0\\0&A+iB}\pmatrix{(i/2)I&(1/2)I\\-(i/2)I&(1/2)I}. $$ Whence $$ \det \pmatrix{A&-B\\B&A}=\det(A-iB)\det(A+iB)=\det(A^2+i(AB-BA)+B^2). $$ If $A$ and $B$ commute, this yields $\det(A^2+B^2)$.

How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$ [duplicate]

Prove that $a^{2^n}=1 \mod 2^{n+2}$

Fields - Proof that every multiple of zero equals zero

Normal distribution tail probability inequality

$\cos(\arcsin(x)) = \sqrt{1 - x^2}$. How?

The number of ways of writing an integer as a sum of two squares

Spectrum of the sum of two commuting matrices

Fast Way of Finding The Remainder

Solving the recurrence $T(n) = \sqrt n T(\sqrt{n}) + \sqrt{n}$

If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$

Proving that $ f: [a,b] \to \Bbb{R} $ is Riemann-integrable using an $ \epsilon $-$ \delta $ definition.

Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289