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Multiplication of Matrices

the matrix A(...

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the matrix A(I+A)^-1 IS EQUAL TO( IS |A| IS NOT EQUAL TO 0 ,|I+A| IS NOT EQUAL TO 0) (1)(A^-1+I)^-1 (2) A^-I (3)(I+A)A (4)(A^-1 +I)^-1A

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\sum_{i = 1}^{90} a i (i + 1)

n \sum i = 1 {\to a}_{i} = 0

∣ ∣ {\to a}_{i} ∣ ∣ = 1, \forall i,

then the value of

\sum 1 \leq i < j \leq n \sum {\to a}_{i} . {\to a}_{j}

A_{i} = [\begin{matrix} a^{i} & b^{i} b^{i} & a^{i} \end{matrix}]

| a | < 1, | b | < 1

\sum_{i = 1}^{\infty} | A_{i} |

\infty \sum i = 1 \infty \sum j = 1 \infty \sum k = 1 \frac{1}{a^{i + j + k}}

(where | a | > 1)

\sum_{i = 1}^{\infty} \sum_{j = 1}^{\infty} \sum_{k = 1}^{\infty} \frac{1}{a^{i + j + k}}

is equal to (where

a > 1

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