NDA 2019 Maths · Mathematics · Determinants · medium

If A and B are 3×3 matrices with |A|=2 and |B|=3, then |2A^-1B| equals

Single correct option

A

and

B

are

3\times3

matrices with

|A|=2

and

|B|=3

, then

|2A^{-1}B|

equals

Show answer and solution

Answer: (A) $12$

Use

|kM|=k^3|M|

for a

3\times3

matrix,

|A^{-1}|=\dfrac1{|A|}

and

|MN|=|M||N|

. Then

|2A^{-1}B|=2^3\cdot\dfrac12\cdot3=8\times\dfrac12\times3=12

. The value

3

forgets the scalar's factor

2^3

, and

24

forgets to invert

A

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake