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# Show that the matrix satisfies the equation A^{3} – 4A^{2} + A = 0.

Answer :

Given:

To show that

Now, we will find the matrix for A^{2}, we get

[as c_{ij} = a_{i1}b_{1j} + a_{i2}b_{2j} + … + a_{in}b_{nj}]

Now, we will find the matrix for A^{3}, we get

So,

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

[as r_{ij} = a_{ij} + b_{ij} + c_{ij}]

Therefore,

Hence matrix A satisfies the given equation.

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