If cap A is equal to the 3 by 3 matrix, row 1, column 1, 3 column 2, negative 1 column 3, 5 row 2, column 1, 2 column 2, 9 column 3, 3 row 3, column 1, 5 column 2, 3 column 3, 1 and cap b is equal to the 3 by 3 matrix, row 1, column 1, 5 column 2, 3 column 3, 1 row 2, column 1, 2 column 2, 9 column 3, 3 row 3, column 1, 3 column 2, negative 1 column 3, 5 , then which statement is true?
Answer
A
det times cap A is equal to negative det times cap b
B
det times cap A is not equal to 0 A n d det cap b is equal to 0
C
det times cap A is equal to det times cap b
D
det times cap A is equal to 0 A n d det cap b is not equal to 0
Explanation
Matrix B is obtained from matrix A by swapping the first and third rows, while leaving the second row unchanged. Swapping two rows changes the sign of a determinant, so det(B) = −det(A), or equivalently det(A) = −det(B). Therefore, the true statement is that det(A) is equal to negative det(B).
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