G Problem 2. (1.4 points) Suppose A is an n × n matrix, such that A 2 + 3A − 4I = 0 where I and 0 are the n × n identity and zero matrix respectively. What can you say about the invertibility of matrix A?

The correct answer is = A + I

Step-by-step explanation:

Since A is an n × n invertible non singular matrix, exists.

Given equation is + 3A -4I = O where I and O are the n × n identity and zero matrix respectively.

⇒ + 3A -4I = O

⇒ ( + 3A -4I ) = × O

⇒ AA + 3 A - 4I = O

⇒ A + 3I - 4 = O

⇒ A + 3I = 4

⇒ = A + I

Thus the value of   can be given by the above equation.