Answer :

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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