Let A be a square matrix of order 3 such that transpose of inverse of A is A itself, then |adj (adj A)| is equal to92741

The given condition is that the transpose of the inverse of matrix A is equal to A itself. This can be written as:

(A^-1)^T = A

Taking determinant on both sides, we get:

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

We know that the determinant of the transpose of a matrix is the same as the determinant of the original matrix. So, we can simplify the left side of the equation to:

|A^-1| = |A|

We also know that the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix. So, we can further simplify the equation to:

1/|A| = |A|

Solving this equation for |A|, we get two possible solutions: |A| = 1 or |A| = -1.

Now, we need to find the value of |adj(adj A)|. We know that the determinant of the adjoint of a matrix is the power of the determinant of the original matrix raised to the order of the matrix minus 1. So, we can write:

|adj(adj A)| = |adj A|^(3-1) = |A|^(3*(3-1)) = |A|^6

Substituting the possible values of |A| into this equation, we get:

|adj(adj A)| = 1^6 = 1 or |adj(adj A)| = (-1)^6 = 1

So, the value of |adj(adj A)| is 1, not 92741.