For the matrix X=\left[\begin{array}{ccc}0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0]\end{array}, (X^2-X) is

CBSE Class 12 Math 2022 Term I Solved Paper - Question 26

Question : 26 of 50

Marks: +1, -0

For the matrix

X={[\table 0 , 1 , 1 ; 1 , 0 , 1 ; 1 , 1 , 0]}, (X^2-X)

Solution:

X^2={[\table 0 , 1 , 1 ; 1 , 0 , 1 ; 1 , 1 , 0]}{[\table 0 , 1 , 1 ; 1 , 0 , 1 ; 1 , 1 , 0]}

⇒ \;\; X^2={[\table 2 , 1 , 1 ; 1 , 2 , 1 ; 1 , 1 , 2]}

⇒ \;\; X^2-X={[\table 2 , 0 , 0 ; 0 , 2 , 0 ; 0 , 0 , 2]}

=2{[\table 1 , 0 , 0 ; 0 , 1 , 0 ; 0 , 0 , 1]}

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