Solve Linear Algebra Questions: Finding Inverses and Determinants"

rabihtawil
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Homework Statement



question 1:
If A is a matrix satisfying 3A^2+6A-I=0, find the inverse of A.

question 2:
Let A be a 3x3 matrix with 4A = A^7. Find the possible values det A.

Homework Equations



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The Attempt at a Solution



this was a very long homework about 17 questions, i solved the others but i got no clue where to start with these, any help is appreciated.

Best Regards.
 
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rabihtawil said:
question 1:
If A is a matrix satisfying 3A^2+6A-I=0, find the inverse of A.
HINT: Multiply through by A-1
rabihtawil said:
question 2:
Let A be a 3x3 matrix with 4A = A^7. Find the possible values det A.
HINTs: det(4A) = 4ndet(A) for an nxn matrix. det(A7) = (det(A))7
 
Or, for question 1, note that 3A^2+ 6A= I so (3A+ 6)A= I.
 
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