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JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Matrices

Let

A = - 1 10 100 - 1 11

satisfy

A^{2} + α (adj (adj (A))) + β (adj (A) (adj (adj (A))))

= 2 - 2 0 - 2 00 2 - 1 - 1

for
Some

α, β \in R

.
Then

(α - β)^{2}

is equal to

Answer: 4

Solution

Here

det A = - 1

. For a

3 \times 3

matrix

adj (adj A) = ∣ A ∣^{n - 2} A = ∣ A ∣ A = - A

, while

adj A \cdot adj (adj A) = ∣ A ∣ (adj A \cdot A) = ∣ A ∣^{2} I = I

. The relation becomes

A^{2} - α A + β I = M

. Since

A^{2} = 2 - 1 0 - 1 10 101

, matching entries with

2 - 2 0 - 2 00 2 - 1 - 1

gives

α = 1

and

β = - 1

. Therefore

(α - β)^{2} = (1 - (- 1))^{2} = 4

.

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Integer answer

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