Question

If A = `[(3, 3),(p, q)]` and A² = 0 find p and q

Answer 1

Given
A = `[(3, 3),(p, q)]`
A² = A x A = `[(3, 3),(p, q)][(3, 3),(p, q)]`

= `[(9 + 3p, 9 + 3q),(3p + pq, 3p + q^2)]`
But A² = 0

∴`[(9 + 3p, 9 + 3q),(3p + pq, 3p + q^2)] = [(0, 0),(0, 0)]`
Comparing the corresponding elements
9 + 3p = 0
⇒ 3p = –9
⇒ p = –3
9 + 3q = 0
⇒ 3q = –9
⇒ q = –3
Hence p = –3, q = –3.