Question

If A = `[(2,1),(-4,-2)]`, then the value of I – A + A² – A³ + ... is ______.

Options

• `[(-1,-1),(4,3)]`

• `[(3,1),(-4,-1)]`

• `[(0,0),(0,0)]`

• `[(1,0),(0,1)]`

Answer 1

If A = `[(2,1),(-4,-2)]`, then the value of I – A + A² – A³ + ... is `underlinebb([(-1,-1),(4,3)])`.

Explanation:

A = `[(2,1),(-4,-2)] I= [(1,0),(0,1)]`

A² = `[(2,1),(-4,-2)][(2,1),(-4,-2)]`

`= [(0,0),(0,0)]`

The value of l − A + A² − A³ ... = `[(-1,-1),(4,3)]`