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Pietro Paparella
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The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], and only uses the criteria stipulated by the OP:

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The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], and only uses the criteria stipulated by the OP:

enter image description here

The following proof appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713] and only uses the criteria stipulated by the OP:

enter image description here

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Pietro Paparella
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The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], and only uses the three criteria stipulated by the OP:

enter image description here

The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], uses the three criteria stipulated by the OP:

enter image description here

The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], and only uses the criteria stipulated by the OP:

enter image description here

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Pietro Paparella
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The following proof, which appears in the recent article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713] and only, uses the three criteria stipulated inby the original post.OP:

enter image description here

The following proof appears in the recent article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713] and only uses the three criteria stipulated in the original post.

enter image description here

The following proof, which appears in the article A Short and Elementary Proof of the Two-sidedness of the Matrix-Inverse [Paparella, P., College Math. J. 48 (2017), no. 5, 366-367; MR3723713], uses the three criteria stipulated by the OP:

enter image description here

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Pietro Paparella
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