Let M and N be two 3 x 3 matrices such that MN = NM. Furthe…

Maths JEE - Advanced Previous Year Paper JEE-Advanced-2014-Paper-1 Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let M and N be two 3 x 3 matrices such that MN = NM. Further, if M N 2 and M 2 = N 4 , then

determinant of (M 2 + MN 2 ) is 0

there is a 3 x 3 non-zero matrix U such that (M 2 + MN 2 )U is the zero matrix

determinant of (M 2 + MN 2 )

for a 3 x 3 matrix U, if (M 2 + MN 2 )U equals the zero matrix then U is the zero matrix

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(a,b)M 2 = N 4 M 2 - N 4 = O (M - N 2 ) (M + N 2 ) = O (As M, N commute.)

Also, M N 2 , Det ((M - N2) (M + N 2 )) = 0

As M + N 2 is not null Det (M + N 2 ) = 0

Also Det (M 2 + MN 2 ) = (Det M) (Det (M + N 2 )) = 0

There exist non-null U such that (M 2 + MN 2 ) U = O

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