can you please explain this question step by step and in details?

KitchenAid carefully tests each of the stand mixer manufactured. Seventy percent of all newly stand mixers are approved, 20% are sent back to be recalibrated, and 10% are determined to be beyond repair and destroyed. Eighty percent of the devices that have been recalibrated are approved, 10% are sent back to be recalibrated again, and 10% are destroyed. Therefore, the four states of stand mixers are New, Approved, Recalibrated, and Destroyed.

Given below are the 4 x 4 absorbing stochastic matrix that describes this transition and the stable matrix, respectively.

A D N R A D N R

A 1 0 0.7 0.8 A 1 0 79/90 8/9

D 0 1 0.1 0.1 D 0 1 11/90 1/9

N 0 0 0 0 N 0 0 0 0

R 0 0 0.2 0.1 R 0 0 0 0

(a) (2 points) Determine the probability that a New stand mixer will eventually be approved. (b) (5 points) Find the Fundamental matrix. You may use a calculator, but must show all the matrices involved. Fully label the fundamental matrix

(b) (5 points) Find the Fundamental matrix. You may use a calculator, but must show all the matrices involved. Fully label the fundamental matrix.

(c) (3 points) Determine the expected number of times a stand mixer will be tested.