Question

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

• A. 125
• B. 625
• C. 75
• D. 375

Answer 1

The Correct Option is B

To find the value of |adj(adjA)| for a 3x3 matrix A where the determinant |A| is given as 5, we use the properties of determinants and adjugates (adjoint matrices).

For a square matrix A of order n, the property of the adjugate is that |adj(A)| = |A|^n-1. Given A is a 3x3 matrix (n=3), |adj(A)| = |A|^3-1 = |A|².

Therefore, |adj(A)| = 5² = 25.

Now, applying the same property to find |adj(adjA)|:

Since adj(adjA) involves another application of the adjugate, we consider an (n-1)th application, yielding: |adj(adjA)| = |adj(A)|^3-1 = |adj(A)|² for a 3x3 matrix.

Thus, |adj(adjA)| = 25² = 625.

Therefore, the value of |adj(adjA)| is 625.