Given:

To prove A² –7A + 10I₃ = 0

Here I₃ is an identity matrix of size 3

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

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

So, Substitute corresponding values in equation

A² –7A + 10I₃, we get

[as r_ij = a_ij + b_ij + c_ij],

Hence the A² –7A + 10I₃ = 0 (Proved)