NDA 2016 Maths · Mathematics · Matrices · hard

If A is a square matrix such that A^2=A, then (I+A)^3 is equal to

Single correct option

A

is a square matrix such that

A^2=A

, then

(I+A)^3

is equal to

Show answer and solution

Answer: (C) $I+7A$

Expand

(I+A)^3=I+3A+3A^2+A^3

, valid because

I

commutes with

A

. Since

A^2=A

, also

A^3=A\cdot A^2=A

. So the sum is

I+3A+3A+A=I+7A

. Forgetting that

A^2

and

A^3

reduce to

A

gives

I+3A

Original question written in the NDA 2016 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