Question

Do you think that every 2x2 matrix has at least one square root? How can I explain this?

Answer 1

Take a look at this

http://en.wikipedia.org/wiki/Square_root_of_a_matrix

look at the part that says "Some matrices have no square root"

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Also, look at this page

http://en.wikipedia.org/wiki/Square_root_of_a_2_by_2_matrix

and search for inside the page "The general formula above fails completely if..."

Answer 2

There isn't any good explanation @jim_thompson5910

Answer 3

I read those already

Answer 4

how about this?

http://faculty.plattsburgh.edu/sam.northshield/sqrtmat3.pdf

Answer 5

@jim_thompson5910 even with that document, it just states that the matrix does not have a square root,

Answer 6

on the bottom of page 1, it says "example 3"

on the next page, they show why it is true

Answer 7

You could always just do a counter example and say no

Answer 8

Thanks @jim_thompson5910 and @FibonacciChick666