NDA 2023 Maths · Mathematics · Matrices · medium

If A is a square matrix with A^2=A, then (I+A)^2 equals

Single correct option

A

is a square matrix with

A^2=A

, then

(I+A)^2

equals

Show answer and solution

Answer: (B) $I+3A$

Since

I

commutes with

A

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

. Substituting

A^2=A

gives

I+3A

. The tempting answer

I+2A

ignores

A^2

, and treating

A^2

0

would be a mistake because idempotent matrices are not nilpotent.

Original question written in the NDA 2023 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