Let A be a non-singular matrix of order 3 such that A a d j 3 A = 5 A A T , then A - 1 3 is equal to

Question

Let A be a non-singular matrix of order 3 such that A a d j 3 A = 5 A A T , then A - 1 3 is equal to,

MARKS App · Accepted Answer

A a d j 3 A = 5 A A T Taking determinant on both sides, we get, A a d j 3 A = 5 A A T ⇒ A 3 A 2 = 5 3 A 2 ⇒ 3 6 A 3 = 5 3 A 2 ⇒ A = 0 , 125 729 A ≠ 0 Hence, A - 1 3 = 1 A 1 3 = 9 5 = 1.8

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