Question 32 of 58intermediate🧠 RememberMCQ1 mark

Let A be a nonsingular square matrix of order 3 ×\times 3. Then |adj A| is equal to

Exercise: EXERCISE 4.4 | Q: 17 | (Page 18)
For More Understanding

Explanation

Option B is correct because according to the general formula provided in the textbook, for a square matrix A of order n, |adj(A)| = |A|^(n-1). Since A is a 3×33 \times 3 matrix, n = 3. Therefore, |adj A| = |A|^(3-1) = |A|^2. The context also explicitly shows this derivation: starting from |(adj A)||A| = |A|^3, dividing both sides by |A| gives |(adj A)| = |A|^2.

Solution Steps

  1. Step 1: Identify that A is a square matrix of order 3, so n = 3.

  2. Step 2: Apply the general formula: |adj(A)| = |A|^(n-1).

  3. Step 3: Substitute n = 3: |adj A| = |A|^(3-1) = |A|^2.

  4. Step 4: The correct option is (B) |A|^2.

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