For all square matrices A, is it true or false that det(−A) = − det(A)

[ari.st]

Are these statements true or false?

• For all square matrices A, det(−A) = − det(A)
  
  
  
• If A and B are square matrices, then det(AB) = det(BA)
  
  
  
• If A and B are square matrices whose columns are the same but in differentorders, then det B = − det A.
  
  
  
• If A is invertible, then det(A−1) = det(AT ).
  
  
• If 0 is the only eigenvalue of a square matrix A, then A is the zero matrix.

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[Deleted member 4993]

Are these statements true or false?

• For all square matrices A, det(−A) = − det(A)
  
  
• If A and B are square matrices, then det(AB) = det(BA)
  
  
• If A and B are square matrices whose columns are the same but in differentorders, then det B = − det A.
• If A is invertible, then det(A−1) = det(AT ).
  
  
• If 0 is the only eigenvalue of a square matrix A, then A is the zero matrix.

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[Steven G]

Are these statements true or false?

• For all square matrices A, det(−A) = − det(A)
  
  
• If A and B are square matrices, then det(AB) = det(BA)
  
  
• If A and B are square matrices whose columns are the same but in differentorders, then det B = − det A.
• If A is invertible, then det(A−1) = det(AT ).
  
  
• If 0 is the only eigenvalue of a square matrix A, then A is the zero matrix.

1. 1. 
      
      
      
   
   
   
   

In order to get help you really need to show us your work. I will supply you with a hint. |AB| = |A|*|B|. This should help you answer some of these problems.