Question

If matrix A = `[(1, -1),(2, 3)]`, then A² – 4A + 5I is where I is a unit matix.

Options

• Null matrix

• Skew symmetric matrix

• Symmetric Matrix

• None of these

Answer 1

Null matrix

Explanation:

Given, A = `[(1, -1),(2, 3)]`

∴ A² = A . A = `[(1, -1),(2, 3)][(1, -1),(2, 3)]`

= `[(1 xx 1 + (-1) xx 2, 1 xx (-1) + (-1) xx 3),(2 xx 1 + 3 xx 2, 2 xx (-1) + 3 xx 3)]`

= `[(1 - 2, -1 - 3),(2 + 6, -2+ 9)]`

= `[(-1, -4),(8, 7)]`

Now, A² – 4A + 5I

= `[(-1, -4),(8, 7)] - 4[(1, -1),(2, 3)] + 5[(1, 0),(0, 1)]`

= `[(-1, -4),(8, 7)] - [(4, -4),(8, 12)] + [(5, 0),(0, 5)]`

= `[(-1 - 4 + 5, -4 + 4 + 0),(8 - 8 + 0, 7 - 12 + 5)]`

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

= 0