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Question

The index of the matrix A -
Where A=[2412]___

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Solution

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

Now all integers greater than this least positive integer will satisfy Am=0.

Since if Am=0

Am+1=0

= Am×A

= 0 × A

= 0

So the least positive integer is the index.

In Question 2

A10

but A2=0

So 2 is that least positive integer which satisfies Am=0. So index of A = 2.


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