Question

If for a square matrix A, A. (adj A) = `[(2025, 0, 0),(0, 2025, 0),(0, 0, 2025)]`, then the value of |A|+ |adj A| is equal to ______.

Options

• 1

• 2025 + 1

• (2025)² + 45

• 2025 + (2025)²

Answer 1

If for a square matrix A, A. (adj A) = `[(2025, 0, 0),(0, 2025, 0),(0, 0, 2025)]`, then the value of |A|+ |adj A| is equal to 2025 + (2025)².

Explanation:

For a square matrix A of order n × n, we have A. (adj A) = |A| I_n, where I_n is the identity matrix of order n × n.

So, A. (adj A) = `[(2025, 0, 0),(0, 2025, 0),(0, 0, 2025)]` = 2025 I₃

⇒ |A| = 2025 and |adj A| = |A|^(3-1) = (2025)²

∴ |A|+ |adj A| = 2025 + (2025)²