Let A = 2 - 1 1 - 2 3 - 2 - 4 4 - x be a matrix. If A 2 = A, then the value of x is equal to

Question

Let A = 2 - 1 1 - 2 3 - 2 - 4 4 - x be a matrix. If A 2 = A, then the value of x is equal to,

MARKS App · Accepted Answer

A 2 = 2 - 1 1 - 2 3 - 2 - 4 4 - x 2 - 1 1 - 2 3 - 2 - 4 4 - x = 2 - 1 4 - x - 2 3 2 x - 8 4 x - 16 16 - 4 x x 2 - 12 ∵ A 2 = A ⇒ 4 - x = 1 ⇒ x = 3 ⇒ 2 x - 8 = - 2 ⇒ x = 3 ⇒ - 4 = 4 x - 16 ⇒ x = 3 ⇒ 4 = 16 - 4 x ⇒ x = 3 ⇒ - x = x 2 - 12 ⇒ x = - 4 or 3 Hence, x = 3

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