If AT A1 which of the following is a possible value for det

If A^T = A^-1, which of the following is a possible value for det(A)? 0 2 -3 5 1

Solution

Given, A^T = A^-1

That means, A is an orthogonal matrix.

Since, A.A^-1 = I (Identity matrix)

This implies A.A^T= I (since A^T = A^-1)

Taking determinant both sides

|A.A^T| = |I|

|A||A^T| = 1 ( since |I| = 1)

|A||A| = 1 ( since |A^T| = |A| )

|A|² = 1

|A| = +1, -1.

Hence, the correct option is E.