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Maths-

General

Easy

Question

If A is non-singular matrix of order 3 × 3, then adj (adj A) is equal to -

|A| A
|A|² A
|A|^–1 A
None of these

The correct answer is: |A| A

As A is a non-singular matrix A^–1 = $fraction numerator 1 over denominator vertical line A vertical line end fraction$ (adj A)
$rightwards double arrow$ adj A = |A| A^–1 = B(say).
Now,
adj (adj A) = adj (B) = |B|B^–1 = ||A|A^–1| (|A| A^–1)^–1
= |A|³ |A^–1| |A|^–1 (A^–1)^–1
= |A|³ $fraction numerator 1 over denominator vertical line A vertical line end fraction$ · $fraction numerator 1 over denominator vertical line A vertical line end fraction$ A
= |A| A.

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