If `A=d i ag\ (a\ \ b\ \ c)` , show that `A^n=d i ag\ (a^n\ \ b^n\ \ c^n)` for all positive integer `n` .

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n.

If A=diag(abc), show that A^(n)=diag(a^(n)b^(n)c^(n)) for all positive integer n .

If A=diag[a,b,c] then show that A^(n)=diag[a^(n),b^(n),c^(n)] for all n in N

Show that a^(n) - b^(n) is divisible by a – b if n is any positive integer odd or even.

Using mathematical induction prove that (d)/(dx)(x^(n))=nx^(n-1) for all positive integers n.

If A and B are square matrices of the same order and A is non-singular,then for a positive integer n,(A^(-1)BA)^(n) is equal to A^(-n)B^(n)A^(n) b.A^(n)B^(n)A^(-n) c.A^(-1)B^(n)A d.n(A^(-1)BA)

Show that a^(n) - b^(n) is divisible by (a + b) when n is an even positive integer. but not if n is odd.

Show that the expression (n^5)/(5) + (n^3)/(3) + (7n)/(15) is a positive integer for all n in N .

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A

(x+1) is a factor of x^(n)+1 only if n is an odd integer (b) n is an even integer n is a negative integer (d) n is a positive integer