Adjoints and Determinants Problem

I need help with this problem, i am totally lost. See attachment. Please explain.
 

Attachments

What have you tried so far? Perhaps use the famous formula that A-1=[1/det(A)]adj(A).
Also note that det(adj(A)) = det(A)n-1 where n is the size of A
 
1,096
2
You need to think about what the adjoint of A is...

The adjoint of A is simply the matrix of cofactors.

So if you took matrix A and did an expansion across the 3rd row to compute its determinant what are you really doing?

Well you're taking the entries 3, -1, -1, multiplying each of them by their respected cofactors and summing them to get the determinant.

How can you relate the desired cofactors to the adjoint? (I stated the answer above)
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top