The notation ak meas the matrix a multiplied with itself k times (a) for the 2×2 identity matrix i, show that i2 =i (b)for the n×n identity matrix i, show that i2 =i (c) what do you think the enteries of ik are?

Entries of I^k are are also identity elements.

Step-by-step explanation:

a) For the 2×2 identity matrix I, show that I² =I

Hence proved  I² =I

b) For the n×n identity matrix I, show that I² =I

n×n identity matrix is as shown in figure

Elements of identity matrix are

As square of 1 is equal to 1 so for n×n identity matrix I, I² =I

(c) what do you think the enteries of Ik are?

As mentioned above

Any power of 1 is equal to 1 so kth power of 1 is also 1. According to this Ik=I

yes

step-by-step explanation:

yes