Q.

The matrix 1-3-4-1541-3-4 is a nilpotent matrix of index

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a

3

b

2

c

1

d

4

answer is B.

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Detailed Solution

matrix  is a nilpotent matrix of index

We know that,

If Ak=0 ,then A  is a nilpotent matrix of index K

A2=A.A =1-3-4-1341-3-41-3-4-1341-3-4 A2=-1+3-4-3-9+12-4-12+161-3+43+9-124+12-161+3-4-3-9+12-4-12+16 A2=0000000003×3 A2=0

 Hence index of Ais K=2

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The matrix 1-3-4-1541-3-4 is a nilpotent matrix of index