Question

In Question 2 what the indexof the matrix A is__

Answer 1

We know that index of a nilpotent matrix is the least positive integer m which satisfies $A^m=0.$

Now all integers greater than this least positive integer will satisfy $A^m=0.$

Since if $A^m=0$

$A^{m+1}=0$

= $A^m\times A$

= 0 $\times$ A

= 0

So the least positive integer is the index.

In Question 2

$A^1\ne 0$

but $A^2=0$

So 2 is that least positive integer which satisfies $A^m=0.$ So index of A = 2.