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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
For invertible linear transformations A and B
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The composition of invertible linear transformations is invertible
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