NDA 2020 Maths · Mathematics · Matrices · medium

If A is a 3×3 matrix with |A|=4, then the value of |2 adj A| is

Single correct option

A

is a

3\times3

matrix with

|A|=4

, then the value of

|2\,\mathrm{adj}\,A|

Show answer and solution

Answer: (C) $128$

For an

n\times n

matrix

|\mathrm{adj}\,A|=|A|^{n-1}=4^2=16

. Also

|kB|=k^n|B|

, so

|2\,\mathrm{adj}\,A|=2^3\cdot16=128

. Forgetting the factor

2^3

gives

16

, and using

|A|^3

for the adjoint gives other wrong values.

Original question written in the NDA 2020 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