Question

If \(A\) is a square matrix of order \(3\) and \(|A| = 5\), find \(|adj(A)|\).

• A. \(5\)
• B. \(10\)
• C. \(25\)
• D. \(125\)

Hint:

Always remember the identity: \[ |adj(A)| = |A|^{n-1} \] where \(n\) is the order of the square matrix. This formula helps quickly evaluate determinants of adjoint matrices.

Answer 1

The Correct Option is C

Concept: For any square matrix \(A\) of order \(n\), the determinant of its adjoint is given by: \[ |adj(A)| = |A|^{\,n-1} \] This is a standard result from matrix theory.

Step 1: Identify the given values. Order of matrix: \(n = 3\) \[ |A| = 5 \]

Step 2: Apply the formula. \[ |adj(A)| = |A|^{n-1} \] \[ |adj(A)| = 5^{3-1} \] \[ |adj(A)| = 5^2 = 25 \]