If for the matrix \A = [\table \alpha, -2;-2,\alpha], |A^3 ...

CBSE Class 12 Math 2022 Term I Solved Paper

Question : 32 of 50

Marks: +1, -0

If for the matrix A=[

α	−2
−2	α

], |A3∣=125, then the value of α is

Solution: 👈: Video Solution

‌ Given, ‌A=[

α	−2
−2	α

]
⇒‌‌|A|=α2−4‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
‌ Also, given ‌‌‌|A3|=125
⇒‌‌|A|3=125
⇒‌‌|A|=5
⇒‌‌α2−4=5‌‌‌ [from eq. (i)] ‌
⇒‌‌α2=9
⇒‌‌α=±3
‌

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