If A is a square matrix such that |A|=-2 , then |AA^ T | , where A^ T is the transpose of A , is equal to

Step-by-step solution

Using the property of determinants, |AB| = |A||B| . Therefore, |AA^ T | = |A||A^ T | . Since the determinant of a matrix is equal to the determinant of its transpose, |A^ T | = |A| . Substituting this into the equation gives |AA^ T | = |A||A| = |A|^2 . Given |A| = -2 , we get |AA^ T | = (-2)^2 = 4 . Answer: 4