Suppose that A and B are 4 × 4 matrices such that B is non-singular. Which of the following statement(s) is/are correct?
1. det(−3A T ) = 34 det(A) and det(A) = det(BAB−1 ).
2. det(3B −1 ) = 34 det(B) and det(A) = det(BAB−1 ).
3. det(2A T ) = −16 det(A) and det(A) = det(BAB−1 ).
4. det(2A T ) = 23 det(A) and det(A) = det(BAB−1 ).
Using the multiplicativity of the determinant, we have:
, therefore,
Moreover, .
From this we have that statement 1 is correct, but statements 2-4 are not.
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