Suppose A is any 3 × 3 non-singular matrix and (A - 3I) (A - 5I) = O where I = I₃ and O = O₃. If α A + β A⁻¹ = 4I, then α + β is equal to:

Matrices and Determinants: JEE Main 2018 Mathematics question

JEE Main 2018 · 15 Apr, Evening shift · Q4479

JEE Main 201815 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Suppose A is any 3

\times

3 non-singular matrix and ( A

-

3I) (A

-

5I) = O where I = I₃ and O = O₃. If

\alpha

A +

\beta

A⁻¹ = 4I, then

\alpha

\beta

is equal to :