Given: and

To show that

Substitute in , we get

I is identity matrix, so

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 2A, we get

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

[as r_ij = a_ij + b_ij + c_ij],

So,

Hence Proved