If A- - - - - - and A2-I- Find the relation given by a2-I-

A=[ α #160; amp; β #160;; γ #160; amp; α #160; ] A ^ 2 =[ α #160; amp; β #160;; γ #160; amp; α #160; ][ ...

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Multiplication of Matrices

If A= [ α ...

Question

If $A = [\begin{matrix} α & β γ & - α \end{matrix}]$ and $A^{2} = I$ . Find the relation given by $a^{2} = I$ .

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Solution

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α, β, γ \neq 0,

∣ ∣ ∣ ∣ \begin{matrix} α + a_{1} b_{1} & a_{1} b_{2} & a_{1} b_{3} a_{2} b_{1} & β + a_{2} b_{2} & a_{2} b_{3} a_{3} b_{1} & a_{3} b_{2} & γ + a_{3} b_{3} \end{matrix} ∣ ∣ ∣ ∣

= α β γ [1 + \frac{a_{1} b_{1}}{α} + \frac{a_{2} b_{2}}{β} + \frac{a_{3} b_{3}}{γ}]

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