If the determinant of the matrix [ 1 3 0 ]
If the determinant of the matrix
[ 1 3 0 ]
[ 2 6 4 ]
[ -1 0 2 ]
is −p, then what is the value of the determinant of the matrix
[ 2 6 0 ]
[ 4 12 8 ]
[ -2 0 4 ] ?
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Correct answer: (D) -8P
Explanation
Every row of the second matrix is 2 times the corresponding row of the first. Multiplying all three rows of a 3×3 matrix by 2 multiplies the determinant by 2³ = 8, so the new determinant is 8 × (−p) = −8p.