Given:

I is identity matrix so

To show that

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 5A, we get

So,

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

[as r_ij = a_ij + b_ij + c_ij]

Therefore,

Hence proved

We will find A⁴

Multiply both sides by A², we get

As multiplying by the identity matrix, I don’t change anything. Now will substitute the corresponding values we get

Hence this is the value of A⁴