. If A and B are square matrices of order 3 such that
|A| = - 1 ,|B| = 3 , then the determinant of 3 AB is equal to
A: - 9
B: - 27
C: - 81
D: 81
Best Answer
Explanation:
We know that ∣AB∣ = ∣A∣ * ∣B∣
Also for a square matrix of order 3, ∣KA∣=|K|3*∣A∣ because each member of the matrix A is multiplied by k, we will end up with k3 in this scenario.
Therefore, ∣3AB∣ = 33∣A∣∣B∣ = 27(−1)(3) = −81
Final Answer:
The determinant of 3 AB is equal to -81, hence Option (C)
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