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Definition of composition of linear transformations
The composition of linear transformations is a linear transformation
The composition of injective linear transformations is injective
The composition of surjective linear transformations is surjective
The composition of invertible linear transformations is invertible
The inverse of a linear transformation is a linear transformation
The inverse of the inverse of a linear transformation is the original linear transformation
The inverse of a composition reverses the order

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The inverse of the inverse of a linear transformation is the original linear transformation

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The inverse of a linear transformation is a linear transformationClose match
Definition of inverse of a linear transformationClose match
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The matrix of an inverse is the inverse of the matrix representationClose match
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The composition of linear transformations is a linear transformationClose match
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InverseClose match
A linear transformation is invertible if and only if it is injective and surjectiveClose match
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