Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is:

Step-by-step solution

Given A is a 3 3 matrix and |A| = -4 . Using the property of determinants |kA| = k^n |A| where n is the order of the matrix, we get: | A⁻¹ -2 | = |- 1 2 A⁻¹ | = (- 1 2 )^3 |A⁻¹| Since |A⁻¹| = 1 |A| : Substituting |A| = -4 , we get |A⁻¹| = - 1 4 . Therefore, | A⁻¹ -2 | = (- 1 8 ) (- 1 4 ) = 1 32 . Answer: 1 32