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Let A be an nxxn matrix such that A+A^('...

Let `A` be an `nxxn` matrix such that `A+A^(')=O_(nxxn)` then `|I+lamdaA^(2)|geM` where `3M+1` is __

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The correct Answer is:
1
Say `lamda lt 0`
`omega=sqrt(-lamda)`
`:.|I+lamdaA^(2)|=|l-omega^(2)A^(2)|=|l-omegaA||l+omegaA|`
As, `A=-A^(')`
`l-omegaA=l+omegaA^(')=(l+omegaA)^(')implies|l+lamdaA^(2)|=|l+omegaA||l+omegaA|'=|l+omegaA|^(2)ge0`
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