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Question

Let A=100101010 satisfies An=An2+A2I for n3. And trace of a square matrix X is equal to the sum of elements in its principal diagonal. Further consider a matrix 3×3 with its column as 1,2,3 such that A50 1=12525,A50 2=010, A50 3=001 Then,

Trace of A50 equals

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is D 3
AnAn2=A2I
A50=A48+A2I

Further,
A48=A46+A2I
A46=A44+A2I

A4=A2+A2I
_________________
A50=25A224I

Here,
A2=100101010100101010
=100110101

A50=2500252502502524100010001
=10025102501

tr(A50)=1+1+1=3.

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