Let $A = [{a_{ij}}]$ be a square matrix of order 3 such that ${a_{ij}} = {2^{j - i}}$, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + ...... + A10 is equal to :

Question

Let $A = [{a_{ij}}]$ be a square matrix of order 3 such that ${a_{ij}} = {2^{j - i}}$, for all i, j = 1, 2, 3. Then, the matrix A² + A³ + ...... + A¹⁰ is equal to :

$\left( {{{{3^{10}} - 3} \over 2}} \right)A$

$\left( {{{{3^{10}} - 1} \over 2}} \right)A$

$\left( {{{{3^{10}} + 1} \over 2}} \right)A$

$\left( {{{{3^{10}} + 3} \over 2}} \right)A$

Solution

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