Question 71

Let $$A = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$$ and $$B = I + \text{adj}(A) + (\text{adj } A)^2 + \ldots + (\text{adj } A)^{10}$$. Then, the sum of all the elements of the matrix $$B$$ is:

A=[[1,2],[0,1]]. adj(A)=[[1,-2],[0,1]]. (adj A)^n=[[1,-2n],[0,1]].

B=I+adj(A)+...+(adj A)^{10}. Sum: [[11, -2(0+1+...+10)],[0,11]]=[[11,-110],[0,11]].

Sum of elements=11-110+0+11=-88.

The answer is Option (3): -88.

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