JEE Main 2016 · 10 Apr · Shift 1 · Mathematics Q64

MathematicsSingle correct+4 / -1Question 64 of 90

Let A be a 3 × 3 matrix such that $A^2-5A+7I=O$ .

Statement - I : $A^{-1}=\dfrac17(5I-A)$ .

Statement - II : The polynomial $A^3-2A^2-3A+I$ can be reduced to 5(A − 4I).

Then :

Statement-I is true, but Statement-II is false.

Statement-I is false, but Statement-II is true.

Both the statements are true.

Both the statements are false.

Answer and worked solution

Official answer: C

$A(5I-A)=7I$ , so I is true. With $A^2=5A-7I$ , $A^3=18A-35I$ and
$A^3-2A^2-3A+I=18A-35I-10A+14I-3A+I=5A-20I=5(A-4I).$
So II is true too.

JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 64