# If show that A2 –5A + 7I = 0. Use this to find A4.

Given:

I is identity matrix so

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 5A, we get

So,

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

[as rij = aij + bij + cij]

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

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