$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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The determinant is multipliciative

For $A_1, \dots, A_n\in\mathbb{F}$, then $\text{det}(A_1\dots A_n)=\text{det}(A_1)\dots \text{det}(A_n)$.
That is, the map $M_n(\mathbb{F})\to\mathbb{F}$ given by $A\to\text{det}(A)$ is multiplicitive. Moreover, if we restrict ourselves to the set of matrices such that their determinant are not $0$, then the determinant is a group homomorphism

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The determinant is multipliciative

For $A_1, \dots, A_n\in\mathbb{F}$, then $\text{det}(A_1\dots A_n)=\text{det}(A_1)\dots \text{det}(A_n)$.
That is, the map $M_n(\mathbb{F})\to\mathbb{F}$ given by $A\to\text{det}(A)$ is multiplicitive. Moreover, if we restrict ourselves to the set of matrices such that their determinant are not $0$, then the determinant is a group homomorphism

Concepts

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Hypothesis

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Results

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Proof

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concepts
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proof
FullPage
result
concepts
hypothesis
implications
proof

The determinant is multipliciative

For $A_1, \dots, A_n\in\mathbb{F}$, then $\text{det}(A_1\dots A_n)=\text{det}(A_1)\dots \text{det}(A_n)$.
That is, the map $M_n(\mathbb{F})\to\mathbb{F}$ given by $A\to\text{det}(A)$ is multiplicitive. Moreover, if we restrict ourselves to the set of matrices such that their determinant are not $0$, then the determinant is a group homomorphism

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

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The determinant is multipliciative

For $A_1, \dots, A_n\in\mathbb{F}$, then $\text{det}(A_1\dots A_n)=\text{det}(A_1)\dots \text{det}(A_n)$.
That is, the map $M_n(\mathbb{F})\to\mathbb{F}$ given by $A\to\text{det}(A)$ is multiplicitive. Moreover, if we restrict ourselves to the set of matrices such that their determinant are not $0$, then the determinant is a group homomorphism

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon
FullPage
result
concepts
hypothesis
implications
proof