Question

If A and B are square matrices of order 2 such that |A| = 2, |B| = 4 then |2 AB| is equal to - 
1. 16
2. 24
3. 32
4. 64

Answer 1

Correct Answer - Option 3 : 32

Concept:

Property of determinant of a matrix:

• Let A be a matrix of order n × n then det(kA) = kn det(A)

• If A and B are two square matrices then |AB| = |A||B|

 

Calculation:

Given: A and B are square matrices of order 2 such that |A| = 2, |B| = 4 

Here, we have to find the value of |2 AB|

As we know that, if A and B are two determinants of order n, then |AB| = |A||B|

⇒ |2 AB| = |2A||B|

As we know that, if A is a matrix of order n, then |kA| = kn |A|, where k ∈ R.

Here n = 2 So, |2A| = 22 ⋅ |A| = 4|A|

⇒ |2 AB| = |2A||B|

= 4|A||B|

= 4 × 2 × 4

= 32