$ \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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Concepts
If
Only If
proof

Properties of invertible matrices

Let $A$ and $B$ be $n\times n$ functions.
  1. If $A$ is invertible, then so is $A^{-1}$ and $(A^{-1})^{-1}=A$
  2. If $A$ and $B$ are both invertible then so is $AB$ and $(AB)^{-1}=B^{-1}A^{-1}$

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If

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Proof

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Properties of invertible matrices

Let $A$ and $B$ be $n\times n$ functions.
  1. If $A$ is invertible, then so is $A^{-1}$ and $(A^{-1})^{-1}=A$
  2. If $A$ and $B$ are both invertible then so is $AB$ and $(AB)^{-1}=B^{-1}A^{-1}$

Concepts

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If

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Only If

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Proof

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concepts
If
Only If
proof
FullPage
result
Concepts
If
Only If
proof

Properties of invertible matrices

Let $A$ and $B$ be $n\times n$ functions.
  1. If $A$ is invertible, then so is $A^{-1}$ and $(A^{-1})^{-1}=A$
  2. If $A$ and $B$ are both invertible then so is $AB$ and $(AB)^{-1}=B^{-1}A^{-1}$

Concepts

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If

Coming soon

Only If

Coming soon

Proof

Coming soon

Properties of invertible matrices

Let $A$ and $B$ be $n\times n$ functions.
  1. If $A$ is invertible, then so is $A^{-1}$ and $(A^{-1})^{-1}=A$
  2. If $A$ and $B$ are both invertible then so is $AB$ and $(AB)^{-1}=B^{-1}A^{-1}$

Concepts

Coming soon

If

Coming soon

Only If

Coming soon

Proof

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FullPage
result
concepts
If
Only If
proof