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Matrix Algebra - Powers of matrices
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 , where Е – an identity matrix.
If A is a regular (non-singular) matrix, it is possible to enter a negative power of a 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:
E x a m p l e  . Find
S o l u t i o n .