Question

find the rank vallue of the matrix 1 0 0
0 1 0
0 0 1​

Answer 1

Step-by-step explanation:

you diagonalize M then you get M=U−1DU, where D is diagonal. Now, consider M2. This equals U−1DUU−1DU. But UU−1=I. Therefore, M2=U−1D2U. Hopefully you can see now (and it's easy to prove) that MN=U−1DNU. To compute DN, just raise each diagonal element to the Nth power