Maths. Section B1Determinants

Let A = [a_ij]_2×4 and B = [b_ij]_4×2, then |3AB| is equal to

Let $A = [a_{ij}]_{2×4}$ and $B = [b_{ij}]_{4×2}$, then $|3AB|$ is equal to

Answer & explanation

Correct answer: option 1

The correct answer is Option (1) → $3^2|AB|$

Given:

Matrix A is of order 2×4 and B is of order 4×2. So, AB is a 2×2 matrix.

Let C = AB ⇒ C is 2×2

Then, |3AB| = |3C|

For any scalar multiplication of a square matrix of order n×n:

|kC| = kⁿ |C|

Here, k = 3 and order n = 2

⇒ |3C| = 3² × |C| = 9|AB|

So, |3AB| = 9 × |AB|