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JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Matrices

Let

A, B

and C be three

2 \times 2

matrices with real entries such that

B = (I + A)^{- 1}

and

A + C = I

. If

BC = [1 - 1 - 5 2]

and

CB [x_{1} x_{2}] = [12 - 6]

, then

x_{1} + x_{2}

is

(A)2
(B)0✓ Correct
(C)-2
(D)4

Answer: (B)

Solution

From

B = (I + A)^{- 1}

, both

B (I + A) = I

and

(I + A) B = I

. Using

A = I - C

, these become

2 B - B C = I

and

2 B - C B = I

, so

B C = C B

. Hence

C B [x_{1} x_{2}] = B C [x_{1} x_{2}] = [1 - 1 - 5 2] [x_{1} x_{2}] = [12 - 6]

, giving

x_{1} - 5 x_{2} = 12

and

- x_{1} + 2 x_{2} = - 6

. Solving,

x_{2} = - 2

and

x_{1} = 2

, so

x_{1} + x_{2} = 0

.

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Single correct option

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