MHB Very basic binary/number systems questions?

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The forum emphasizes a collaborative approach to learning, encouraging members to share their progress and thoughts when asking questions about binary and number systems. This method allows helpers to provide more effective guidance tailored to the individual's needs. Members are advised to limit their inquiries to two questions per thread to enhance organization and response times. Additionally, if a question has multiple parts, it should be posted in a single thread, while separate threads should be created for other questions. These guidelines are designed to foster a productive environment for both learners and helpers.
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Hello and welcome to MHB, xsparklex! :D

We believe that the best way to help members is to give hints and nudge them in the right direction over the course of multiple posts if necessary. Simply giving out answers is much less effective long-term and we strive to have our members truly improve their mathematical skills. In light of this we ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

Also, we ask that our members do not ask more than two questions in a thread or post. It is better for forum organization, and better for you to get your questions answered in a more timely manner, if you start new threads as necessary for remaining questions. E.g., if you have five questions, post four of them in two threads (two questions each thread) and start a new thread for the remaining one. And if the question has more than two parts to it, it is best to post only that question and its parts in one thread and start a new thread for other questions.

Many people who volunteer their time to help are much more likely to feel inclined to help if there is not a long list of problems, and they can see what you have done so they know how best to help.

I know this may seem like I am barraging you with a long list of rules here on your very first post, but it is not meant to be critical, but merely to inform you of how we do things and why. :D I hope you can see that we have carefully designed our policies to make MHB much more useful for those asking questions and for those helping with questions too.
 
Thread 'Erroneously  finding discrepancy in transpose rule'
Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...

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