Q99 / 180 · COMEDK 2024 (Afternoon Shift) · Mathematics
$\text { If A }(\operatorname{adj} A)=5 I \text {, where I is the identity matrix of order } 3 \text {, then }|\operatorname{adj} A|=$
- Correct answerA25
- B10
- C125
- D5
Solution
Given the property of the adjoint of a matrix, $A(\operatorname{adj} A) = |A|I$.
Comparing this with the given equation $A(\operatorname{adj} A) = 5I$, we find that $|A| = 5$.
The determinant of the adjoint of a matrix of order $n$ is given by $|\operatorname{adj} A| = |A|^{n-1}$.
Here, the order of the matrix $n = 3$.
Substituting the values, $|\operatorname{adj} A| = 5^{3-1} = 5^2 = 25$.
Answer: 25
Comparing this with the given equation $A(\operatorname{adj} A) = 5I$, we find that $|A| = 5$.
The determinant of the adjoint of a matrix of order $n$ is given by $|\operatorname{adj} A| = |A|^{n-1}$.
Here, the order of the matrix $n = 3$.
Substituting the values, $|\operatorname{adj} A| = 5^{3-1} = 5^2 = 25$.
Answer: 25
Hence, the correct answer is option: 'A'.