Question
Let A be a 10×10 matrix such that A5 is null matrix and let I be the 10 × 10 identity matrix. The determinant of A+ I is _____.
Answer :
1
Given :
[A ] 10 ×10
A5 = 0
λ5 = 0
λ = 0
Eigen value of [ A+1]' =λ+ 1=0+1 = 1
Determinant of [ A+1] =1
Hence, the correct answer is 1.
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