If A = beginbmatrix α & 2 \ 2 & α endbmatrix and |A^3| = 125, then the value of α is

If A = beginbmatrix α & 2 \ 2 & α endbmatrix and |A^3| =… — JEE Main 2004 Mathematics PYQ

AIEEE 2004

A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}

and

|A^3| = 125

, then the value of

\alpha

Show answer and solution

Correct option: C

Solution

|A| = α² - 4, so |A³| = |A|³ = (α² - 4)³ = 125. Taking cube root: α² - 4 = 5, giving α² = 9, so α = ±3.

[AIEEE 2004]

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