Question

If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is ______ 

विकल्प

• a³

• a⁶

• a⁹

• a²⁷

Answer 1

If A = `[(a, 0, 0), (0, a, 0), (0, 0, a)]`, then the value of |A| |adj A| is a⁹.

Explanation:

|A| = a³

|A| |adj A| = |A (adj A)| = |A| I

= `|(|A|, 0, 0), (0, |A|, 0), (0, 0, |A|)| = |A|^3 = (a^3)^3 = a^9`