Let A be a 3 × 3 matrix such that A² - 5A + 7I = 0 Statement - I: A⁻¹ = 1/7 (5I - A). Statement - II: The polynomial A³ - 2A² - 3A + I can be reduced to 5(A - 4I). Then:

(C) Both the statements are true.

(A) Statement-I is true, but Statement-II is false.

(B) Statement-I is false, but Statement-II is true.

(D) Both the statements are false

Matrices and Determinants: JEE Main 2016 Mathematics question

JEE Main 2016 · 10 Apr, Morning shift · Q4478

JEE Main 201610 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let A be a 3

\times

3 matrix such that A²

-

5A + 7I = 0 Statement - I : A^

-

1 =

{1 \over 7}

(5I

-

A). Statement - II : The polynomial A³

-

2A²

-

3A + I can be reduced to 5(A

-

4I). Then :