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

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Matrices and Determinants

JEE Main 2016 · 10 Apr, Morning shift · Q4478

MathematicsMedium244×since 2002Q4478

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 :