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JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Matrices

Let

A = (20 - 1 2)

. If

B = I -^{5} C_{1} (adj A) +^{5} C_{2} (adj A)^{2} - \dots -^{5} C_{5} (adj A)^{5}

, then the sum of all elements of the matrix

B

is:

(A)-5
(B)-6
(C)-7✓ Correct
(D)-8

Answer: (C)

Solution

First, compute

adj A = (2012)

. The expression for

B

is the binomial expansion:

B = (I - adj A)^{5}

. We have

I - adj A = (- 1 0 - 1 - 1)

. Computing the fifth power:

(I - adj A)^{5} = (- 1 0 - 5 - 1)

. The sum of all elements is

- 1 + (- 5) + 0 + (- 1) = - 7

.

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Single correct option

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