Determinants Matrices Question 86
Question: If the matrix B is the adjoint of the square matrix A and $ \alpha $ is the value of the determinant of A, then what is AB equal to-
Options:
A) $ \alpha $
B) $ ( \frac{1}{\alpha } )I $
C) $ I $
D) $ \alpha I $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Since, adjoint of the square matrix A is B
$ \Rightarrow \frac{B}{| A |}={A^{-1}} $
$ \Rightarrow \frac{AB}{| A |}=A{A^{-1}}=I $
$ \Rightarrow AB=| A |I\Rightarrow AB=\alpha I $
BETA
