Matrices: Show B^3 = B?

Posted on 2017-03-17 18:31:00 in Math by IVAN

Hi, I'm trying to figure out how to describe a matrix problem I saw online. 

Here is the problem. 

Let B = {-1 0} 
{ 2 1} 

(a) Show that B^3 = B. 
(b) Use (a) to show that B^27 = B without doing any more matrix multiplication. 

So, I can multiply it manually, and the answer always seems to be equal to itself so long as it's multiplied by a multiple of the power of 3. If multiplied by a multiple of the power of 2, it is just an identity matrix. 

How would I go about showing these two problems, without actually having to go through the process of showing the manual multiplying of the matrix. 

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