Question

If A is a square matrix such that A(adjA) = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then `(|adj(adjA)|)/|adjA|` is equal to ______.

Options

• 7.00

• 8.00

• 9.00

• 10..

Answer 1

If A is a square matrix such that A(adjA) = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then `(|adj(adjA)|)/|adjA|` is equal to 9.00.

Explanation:

= A(adjA) = |A|I₃ = `3[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

⇒ |A| = 3

|adj(adjA)| = `3^((3–1)^2)` = 3⁴

|adjA| = 3^(3–1) = 3²

⇒ `(|adj(adjA)|)/|adjA| = 3^4/3^2` = 3² = 9