Mathematical Thinking - Matrices

[punchline]

Hi guys! iv been stuck on this question for a while now, could anyone give me a hand?

construct a counter example for the statement:

For matrices A with real entries: "A^3=Identity implies A=identity"

thank you too anyone that lends a hand!

 

[stapel]

Hi guys! iv been stuck on this question for a while now, could anyone give me a hand?

construct a counter example for the statement:

For matrices A with real entries: "A^3=Identity implies A=identity"

thank you too anyone that lends a hand!

What have you tried? You're not restricted on size, so you probably started with 2-by-2 matrices. How far did you get? Where are you stuck?

Please be complete. Thank you!

 

[punchline]

I am very new with matrices and i have tried 2x2 and 3x3 examples. I even tried solving with algebra, (a,b,c,d)^3 see what i got and it just seemed like a equation with many solutions.

i have found examples for imaginary numbers but i can see a link.

any hints? very stuck

 

[stapel]

I am very new with matrices and i have tried 2x2 and 3x3 examples. I even tried solving with algebra, (a,b,c,d)^3 see what i got and it just seemed like a equation with many solutions.

i have found examples for imaginary numbers but...k

What examples have you found? When working with real numbers, have you considered methods such as "Example 2" here or here?

 

[punchline]

oh wow! i had forgotten that you could represent rotations with matrix's. thank you!