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
Taking determinants of AB = 3I and using \(\det(AB) = \det(A)\det(B)\):
\(\det(A)\det(B) = \det(3I)\)
For a matrix of order n, \(\det(kM) = k^n\det(M)\). Here n = 3 and \(\det I = 1\):
\(\det(3I) = 3^3 = 27\)
\(3\det(B) = 27\)
\(\det(B) = 9\)
Tip: A scalar comes out of a determinant raised to the order: \(\det(3I) = 27\) for order 3, not 3.