If `A= ((3,-4),(1,-1))`, then prove by Mathematical Induction that : `A^n = ((1+2n,-4n),(n,1-2n))`, where `n in N`

If A= ((-1,-4),(1,3)) , then prove by Mathematical Induction that : A^n = ((1-2n,-4n),(n,1+2n)) , where n in N

If A= ((11,-25),(4,-9)) , then prove by Mathematical Induction that : A^n = ((1+10n,-25n),(n,1-10n)) , where n in N

By Mathematical Induction, prove that : n! 1 .

Prove the following by the principle of Mathematical Induction: If A = {:[(3,-4),(1,-1)], then A^n = [(1+2n, -4n),(n,1-2n)] where n in N.

Prove by mathematical induction that 1+3+3^2+…………+3^(n-1)=(3^n -1)/2

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Prove by mathematical induction that 10^(2n-1)+1 is divisible by 11

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

Prove, by Mathematical Induction, that for all n in N, 3^(2n)-1 is divisible by 8.