Show that the matrix satisfies the equation A3 – 4A2 + A = 0.
Given:
To show that
Now, we will find the matrix for A2, we get
[as cij = ai1b1j + ai2b2j + … + ainbnj]
Now, we will find the matrix for A3, we get
So,
Substitute corresponding values from eqn(i) and (ii), we get
[as rij = aij + bij + cij]
Therefore,
Hence matrix A satisfies the given equation.