Question

Matrix A = `[(6, 9),(-4, k)]` such that A² = `[(0, 0),(0, 0)]`. Then k is ______.

Options

• 6

• –6

• 36

• ± 6

Answer 1

Matrix A = `[(6, 9),(-4, k)]` such that A² = `[(0, 0),(0, 0)]`. Then k is –6.

Explanation:

Compute A² = A × A   ...(Use matrix multiplication)

A = `[(6, 9),(-4, k)]`

So, A² = `[(36 + 9(-4), 6 × 9 + 9k),((–4) × 6 + k(–4), (–4) × 9 + k^2)]` 

= `[(0, 54 + 9k),(-24 − 4k, k^2 - 36)]`

For A² to be the zero matrix we need 54 + 9k = 0 and −24 − 4k = 0, both give k = –6. 

Although k² – 36 = 0 allows k = ±6, the off-diagonal equations force k = –6.