Let A and B be 3 * 3 matrices, with det(A) = 2, det(B) = 3.
Then det(5 A B^{-1}) =
a) none of these
b) 30
c) 250/3
d) 10/3
e) 2/3
since
|B-1| = 1/|B|,
|AB| = |A|*|B|
|nA| = n^2 |A|,
the results is
5 * 2 * 1/3 = 10/3
Better study up some more on properties of determinants.
To find the determinant of a matrix, we can use the properties of determinants.
First, let's recall some properties of determinants:
1. det(A * B) = det(A) * det(B)
2. det(A^{-1}) = 1 / det(A)
Given that det(A) = 2 and det(B) = 3, we want to find the determinant of the matrix 5AB⁻¹.
Using property 1, we can rewrite the expression as:
det(5AB⁻¹) = det(5A) * det(B⁻¹)
Now, let's find the determinant of B⁻¹. Using property 2, we have:
det(B⁻¹) = 1 / det(B) = 1 / 3
Substituting this back into the expression, we have:
det(5AB⁻¹) = det(5A) * (1 / 3)
Now, we need to find the determinant of 5A. Using property 1, we have:
det(5A) = 5 * det(A) = 5 * 2 = 10
Substituting this back into the expression, we have:
det(5AB⁻¹) = 10 * (1 / 3) = 10/3
Therefore, the answer is d) 10/3.
Actually
|nA| = n^3 |A| because it is a 3*3 matrix.
Seems like you better study up some more on properties of determinants