Question

If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A² – 5A)A^–1 = ______.

विकल्प

• `[(4, 2, 3),(-1, 4, 2),(1, 2, 1)]`

• `[(-4, 2, 3),(-1, -4, 2),(1, 2, -1)]`

• `[(-4, -1, 1),(2, -4, 2),(3, 2, -1)]`

• `[(-1, -2, 1),(4, -2, -3),(1, 4, -2)]`

Answer 1

If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A² – 5A)A^–1 = `underlinebb([(-4, 2, 3),(-1, -4, 2),(1, 2, -1)]`.

Explanation:

(A² – 5A)A^–1 = A²A^–1 – 5AA^–1

= A.AA^–1 – 5I

= A – 5I

= `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)] - [(5, 0, 0),(0, 5, 0),(0, 0, 5)]` 

= `[(-4, 2, 3),(-1, -4, 2),(1, 2, -1)]`