Home
Class 12
MATHS
Let m and N be two 3x3 matrices such tha...

Let m and N be two 3x3 matrices such that MN=NM. Further if `M!=N^2` and `M^2=N^4` then which of the following are correct.

A

determinant of `(M^(2)+MN^(2))` is 0.

B

there is a `3 times 3` non-zero matrix U such that `(M^(2)+MN^(2))U` is the zero matrix.

C

determinant of `(M^(2)+MN^(2)) ge 1`

D

for a `3 times 3` matrix U, if `(M^(2)+MN^(2))U` equals the zero matrix then U is the zero matrix.

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2015|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2016|5 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2013|2 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

Similar Questions

Explore conceptually related problems

Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that Mn=NM . If P^(T) denotes the transpose of P, then M^(2) N^(2) (M^(T)N)^(-1) (MN^(-1))^(T) is equal to

Factroise the following. 14mn^2 (2m-n)

A=[{:(a,b),(b,-a):}] and MA=A^(2m) , m in N for some matrix M , then which one of the following is correct ?

Let us find the factor of the following algebraic expressions. 5mn, 6n^2, 71 m^2

Lets us find the factor of the following algebraic expressions. 121 mn (m^2 - n)

Consider a point A(m,n) , where m and n are positve intergers. B is the reflection of A in the line y=x , C is the reflaction of B in the y axis, D is the reflection of C in the x axis and E is the reflection of D is the y axis. The area of the pentagon ABCDE is a. 2m (m+n) b. m (m+3n) c. m(2m+3n) d. 2m(m+3n)

(i) Write two differences between orbit and orbital. (ii) Two sets of four quantum numbers of an electron are: (n=4 , l=3, m=3, s=(1)/(2) ) and n=3, l=2, m=-2, s=0). Which one of these sets is not correct and why?

Let m and n be two positive integers greater than 1. if lim_(alphararr0)((e^cos(a^n)-e)/alpha^m)=-(e/2) ,then the value of m/n is

Let l_(1),m_(1),n_(1),l_(2),m_(2),n_(2)" and "l_(3),m_(3),n_(3) be the durection cosines of three mutually perpendicular lines. Show that the direction ratios of the line which makes equal angles with each of them are (l_(1)+l_(2)+l_(3)),(m_(1)+m_(2)+m_(3)),(n_(1)+n_(2)+n_(3)) .

A rectangle with sides of lengths (2n-1) and (2m-1) units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) m^2n^2 (b) mn(m+1)(n+1) (c) 4^(m+n-1) (d) non of these