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JEE Main · 2007 · 29 Apr 2007 · Offline · Determinants

Let

A = 500 5 α α 0 α 5 α 5

. If

A^{2} = 25

, then

∣ α ∣

equals

(A) $5^{2}$
(B) $1$
(C) $1/5$ ✓ Correct
(D) $5$

Answer: (C)

Solution

The matrix is upper triangular, so its determinant is the product of the diagonal entries,

∣ A ∣ = 5 \cdot α \cdot 5 = 25 α

. Then

∣ A^{2} ∣ = ∣ A ∣^{2} = 625 α^{2}

, and setting this equal to

25

gives

α^{2} = \frac{1}{25}

. Hence

∣ α ∣ = \frac{1}{5}

.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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