Let $G$ be a finite subgroup of $\mathrm{GL}_n(\mathbb{k})$ where $\mathbb{k}$ is an algebraically closed field. Choose the correct statement(s) from below: (A) Every element of $G$ is diagonalizable; (B) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{Q}$; (C) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{F}_p$; (D) There exists a basis of $\mathbb{k}^n$ with respect to which every element of $G$ is a diagonal matrix.
Let $G$ be a finite subgroup of $\mathrm{GL}_n(\mathbb{k})$ where $\mathbb{k}$ is an algebraically closed field. Choose the correct statement(s) from below:\\
(A) Every element of $G$ is diagonalizable;\\
(B) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{Q}$;\\
(C) Every element of $G$ is diagonalizable if $\mathbb{k}$ is an algebraic closure of $\mathbb{F}_p$;\\
(D) There exists a basis of $\mathbb{k}^n$ with respect to which every element of $G$ is a diagonal matrix.