Given:

I₂ is an identity matrix of size 2, so

Also given,

Now, we will find the matrix for A², we get

[as c_ij = a_i1b_1j + a_i2b_2j + … + a_inb_nj]

Now, we will find the matrix for kA, we get

So,

Substitute corresponding values from eqn(i) and (ii), we get

[as r_ij = a_ij + b_ij + c_ij],

And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal

Hence,

Therefore, the value of k is 1