Question

If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.

Options

• - 2 l

• 2 l

• 5 l

• 4 l

Answer 1

If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = 4 l.

Explanation:

We have , A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`

∴ |A| = `|(1 + 2"i", "i"),(- "i", 1 - 2"i")|`

= (1 + 2i)(1 - 2i) + i²

= 1 - (2i)² + (- 1)

= 1 + 4 - 1 = 4

∴ A(adj A) = |A| l = 4 l