# I've spent 6 hours, still can't get it.

• hola
In summary, there could be various reasons for being unable to solve a problem after 6 hours, such as a lack of understanding, incorrect approach, or missing information. It is important to carefully assess the situation and try different strategies, such as breaking down the problem, seeking help, and staying organized. Resources such as textbooks, online tutorials, and mentors can also be helpful. When struggling, it is important to stay motivated and persevere, even if it means taking breaks or seeking support. If the problem still cannot be solved after 6 hours, it may be helpful to reassess the approach and seek further assistance.
hola
B is a n*n matrix

1. Let B^2 =B. Prove that either det(B) =1 or B is singular.
2. If Transpose(B) = B^-1 , what is det(B)?

If b^2=b, then det(b^2)=det(b)^2=det(b), which has two solutions for det(b). For the second part, since a singular matrix doesn't have an inverse, you are forced into the only allowed non-zero determinant.

I understand that you have spent 6 hours trying to solve this problem, and it can be frustrating when things don't come easily. Don't worry, sometimes it takes time and effort to fully understand and solve a problem. Keep persevering and don't give up.

1. To prove that either det(B) = 1 or B is singular, we can use the fact that if B^2 = B, then B is an idempotent matrix. This means that B^2 - B = 0. We can then use the determinant property that det(AB) = det(A)det(B) to get det(B^2 - B) = det(0), which equals 0. Therefore, det(B^2 - B) = 0 and we can factor out det(B) to get det(B)(det(B) - 1) = 0. This means that either det(B) = 0 or det(B) = 1. If det(B) = 0, then B is singular. If det(B) = 1, then we have proven the statement.

2. If transpose(B) = B^-1, then B is an orthogonal matrix. This means that B^T = B^-1 and det(B^T) = det(B^-1) = 1/det(B). From this, we can see that det(B) = 1 or -1. However, since B is an orthogonal matrix, it must have real eigenvalues. This means that det(B) cannot equal -1, so we are left with det(B) = 1.

## What could be causing the issue?

There could be a variety of reasons why you are unable to solve the problem after 6 hours. It could be due to a lack of understanding of the topic, incorrect approach, or missing information. It is important to carefully assess the situation and try different approaches to identify the root cause.

## Is there a specific method or strategy that could help me solve the problem?

Every problem is unique and may require a different approach. Some general strategies that can help include breaking down the problem into smaller parts, seeking help from others, and taking breaks to clear your mind. It is also important to stay organized and keep track of your progress.

## What resources can I use to help me solve the problem?

There are many resources available to help you solve a problem. Some options include textbooks, online tutorials, forums, and asking for guidance from a mentor or colleague. It is important to use reliable and credible sources to ensure accurate information.

## How can I stay motivated when I'm struggling to solve the problem?

Solving a difficult problem can be frustrating and demotivating, but it is important to stay positive and persevere. You can try taking a break, practicing self-care, or seeking support from friends or colleagues. Remember that every challenge is an opportunity to learn and grow.

## What should I do if I still can't solve the problem after 6 hours?

If you are still unable to solve the problem after 6 hours, it may be helpful to take a step back and reassess your approach. You can also seek help from others or consult additional resources. Remember to stay patient and persistent, as problem-solving often takes time and effort.

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