Question

If A = `[(1, 1),(x, x)]`,find the value of x, so that A² – 0

Answer 1

Given
A = `[(1, 1),(x, x)]`

A² = `[(1, 1),(x, x)][(1, 1),(x, x)]`

= `[(1 + x, 1 + x),(x + x^2, x + x^2)]`
∵ A² = 0

∴ = `[(1 + x, 1 + x),(x + x^2, x + x^2)]` = 0

= `[(0, 0),(0, 0)]`
Comparing
1 + x = 0
⇒ x = –1.