How do you multiply #((2, -1), (3, 4))^4#?

1 Answer
Ananda Dasgupta
Mar 22, 2018

#((-107, -84),(252,61)) #

Explanation:

Just like with ordinary numbers #A^4 = A times A times A times A#. This looks like it may take three matrix multiplications, but we can actually do this in 2.

#A = ((2, -1), (3, 4)) implies#
#A^2 = ((2, -1), (3, 4))((2, -1), (3, 4)) = ((1, -6),(18,13))#
and thus
#A^4 =A^2 times A^2 = ((1, -6),(18,13))((1, -6),(18,13)) =((-107, -84),(252,61)) #

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