If compute A² – 4A + 3I₃.

Given:

To find the value of A² – 4A + 3I₃

I₃ is an identity matrix of size 3, 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 4A, we get

So, Substitute corresponding values from eqn(i) and (ii)in equation A² – 4A + 3I₃, we get

[as r_ij = a_ij + b_ij + c_ij],

Hence the value of