JEE Main2005MathematicsMathematical InductionActual
If A= [ array ll 1 & 0 1 & 1 array ] and I= [ array ll 1 & 0 0 & 1 array ] , then which one of the following holds for all n 1 , by the principle of mathematical indunction
Options
- AA^n=n A-(n-1) I
- BA^n=2^ n-1 A-(n-1) I
- CA^n=n A+(n-1) I
- DA^n=2^ n-1 A+(n-1) I
Correct answer
A. A^n=n A-(n-1) I
Step-by-step solution
By the principle of mathematical induction (A) is true.