Question

If A is a square matrix of order 4 and |adj A| = 27, then A (adj A) is equal to ______.

Options

• 3

• 9

• 3I

• 9I

Answer 1

If A is a square matrix of order 4 and |adj A| = 27, then A (adj A) is equal to 3I.

Explanation:

We know that A ⋅ (adj A) = |A|I

Formula: |adj (A)| = |A|ⁿ⁻¹

Where n is the order of the matrix.

Since A is of order 4, therefore n = 4

Thus, |adj (A)| = |A|ⁿ⁻¹

27 = |A|⁴⁻¹

27 = |A|³

3³ = |A|³

|A| = 3

Now, A ⋅ (adj A) = |A|I

Putting |A| = 3

A ⋅ (adj A) = 3I