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Powers of matrices
Let A – a square matrix and n – a natural number. Then the n -th power of the matrix A is:
Besides it is considered, that
– an identity matrix.
For powers of matrices with the whole indices the following rules take place:
If A and B – square matrices of the same orders, and АВ = ВА , then Newton’s binomial formula takes place:
S o l u t i o n .