Question

Let $A$ be a square matrix of order 3. If $|A| = 5$, then $|adj A|$ is:

• A. 5
• B. 120
• C. 25
• D. 5

Hint:

The determinant of the adjoint matrix is related to the determinant of the original matrix by $|adj A| = |A|^{n-1}$ where $n$ is the order of the matrix.

Answer 1

The Correct Option is C

The determinant of the adjoint of a matrix $A$ is given by: \[ |adj A| = |A|^{n-1} \] where $n$ is the order of the matrix. Here $|A| = 5$ and the order of the matrix is 3, so: \[ |adj A| = |A|^{3-1} = 5^2 = 25 \] Thus, $|adj A| = 25$.