Q69 / 150 · MHT CET 2019 (02 May Shift 1) · Mathematics

If $A$ is non-singular matrix such that $(A - 2 I) (A - 4 I) = 0$ , then $A + 8 A^{- 1} =$ ________

A
$I$
B
$0$
C
$3 I$
Correct answer
D
$6 I$

Solution

Given:

A

is non-singular matrix then

|A| \neq 0

Also

(A - 2 I) (A - 4 I) = 0

A^{2} - 6 A + 8 I = 0 m u l t i p l y b y A^{- 1}

both the side

W e h a v e A + 8 A^{- 1} = 6 I

Hence, the correct answer is option: 'D'.

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