This might help:
As for the determinant:
consider the matrix M= (2 0, 0 2)^n, for n>1 ; n E 1.
Calculate M^n for n= 1, 2, 3, 4, 5, 10, 20, 50. describe any pattern observed, and generalize the pattern into an expression for the matrix M^n in terms of n.
Determine detM for the powers of the matrices calculated above. Describe any pattern observed, generalize the pattern into an expression for det(M^n) in terms of n.
HELP please!>?. Thanks in advance.