Question

If A is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A^-1 = ______.

Options

• l

• 0

• 3l

• 6l

Answer 1

If A is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A^-1 = 6l.

Explanation:

We have, IAI ≠ 0

⇒ A^-1 is exists.

Since, (A - 2l) (A - 4l) = 0

⇒ A² - A(4l) - 2l( ) + Bl · l = 0

⇒ A² - 4AI - 2Al + 8l = 0

⇒ A² - 6Al + 8l = 0

⇒ A² - 6A + 8l = 0

On pre multiply both sides by A^-1, we get

A^-1A² - 6A^-1 A + aA^-1l= 0

⇒ lA - 6l + 8A^-1 = 0

⇒ A - 6l + 8A^-1 = 0 

⇒ A + 8A^-1 = 6l