How to calculate matrixA^100 manually

[promisedhl]

hi guys...my teacher wants me to calculate A^100 of a 3*3 matrix by hand...i can't use MATLAB for this...how do i do it...i can't imagine multiplying 100 time...
help me

 

[Borek]

(A^50)^2

But most likely this is a specific matrix, with interesting properties that make it easy to calculate power no matter how high.

 

[JSuarez]

Check if the matrix is diagonalizable or, if it isn't, use the Jordan form to write it as a sum of a diagonal plus nilpotent matrix.

 

[promisedhl]

thanks guys...will try all

 

[bpet]

Yet another way is to use the minimal polynomial to express A^100 in terms of I, A, A^2.

 

[promisedhl]

i actually did it by finding the eigen values of the matrix...
anyways thank u guys for responding