If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9
Given:
\(\det(A) = 3\)
\(AB = 3I\), where \(I\) is the identity matrix of order 3
Take determinant on both sides:
\[ \det(AB) = \det(3I) \]
Since \(\det(AB) = \det(A) \cdot \det(B)\), and \(\det(kI) = k^n\) for \(n \times n\) matrix:
\[ \det(A) \cdot \det(B) = 3^3 = 27 \]
Substitute \(\det(A) = 3\):
\[ 3 \cdot \det(B) = 27 => \det(B) = \frac{27}{3} = 9 \]