Let E and M be 3×3 matrices satisfying the system of equations EMT=(EM)T=20I , (E+M)T=17(E−M)T Where I denote the Identity matrix of order 3 . if E2+M2=abI (where a and b are coprime) then the value of [a+b100] is (where [x] denote the greatest integer ≤ x)

16ET=18MT⇒16E=18MEM=20I⇒E2+M2=72518I⇒a+b=743

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Let E and M be $3 \times 3$ matrices satisfying the system of equations $E M^{T} = {(E M)}^{T} = 20 I$ , ${(E + M)}^{T} = 17 {(E - M)}^{T}$ Where $I$ denote the Identity matrix of order 3 . if $E^{2} + M^{2} = \frac{a}{b} I$ (where a and b are coprime) then the value of $[\frac{a + b}{100}]$ is (where [x] denote the greatest integer $\leq$ x)

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$16 E^{T} = 18 M^{T} \Rightarrow 16 E = 18 M$

$E M = 20 I \Rightarrow E^{2} + M^{2} = \frac{725}{18} I \Rightarrow a + b = 743$

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