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Answer:
Hey mate here is your answer
Answer is A
Step-by-step explanation:
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Answer:
A³ - 35A = A
Step-by-step explanation:
Given,
A = [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex]
⇒ A = 2[2(2)-2(2)] - 2[2(2)-2(2)] + 2[2(2)-2(2)]
⇒ A = 2[0] - 2[0] + 2[0]
⇒ A = 0
A³ = [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex] [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex] [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex]
⇒ A³ = [tex]\left[\begin{array}{ccc}2(2)&2(2)&2(2)\\2(2)&2(2)&2(2)\\2(2)&2(2)&2(2)\end{array}\right][/tex] [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex]
⇒ A³ = [tex]\left[\begin{array}{ccc}4&4&4\\4&4&4\\4&4&4\end{array}\right][/tex] [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex]
⇒ A³ = [tex]\left[\begin{array}{ccc}4(2)&4(2)&4(2)\\4(2)&4(2)&4(2)\\4(2)&4(2)&4(2)\end{array}\right][/tex]
⇒A³ = [tex]\left[\begin{array}{ccc}8&8&8\\8&8&8\\8&8&8\end{array}\right][/tex]
Evaluate the value of det,
⇒ A³ = 8(8(8)-8(8)) - 8(8(8)-8(8)) + 8(8(8)-8(8))
⇒ A³ = 8(0) - 8(0) + 8(0)
⇒ A³ = 0
now, evaluate '35A'
⇒ 35A = 35 [tex]\left[\begin{array}{c,c,c}2&2&2\\2&2&2\\2&2&2\end{array}\right][/tex]
⇒ 35A = 35(0) = 0
so, ∴ A³ - 35A = 0 - 0 = 0 = A
HOPE THIS WOULD BE HELPFUL FOR YOU