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Question

A real 4×4 matrix A satisfies the equation A2=I, where I is the 4×4 identity matrix. The positive eigen value of A is.

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Solution

A2=I ...(1)
We know that AA1=I ...(2)
From (1) and (2)
A=A1
If λ is an eigen value of matrix A then
λ=1λ
λ2=1
λ=±1
Positive eigen value of A =1.

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