Answer :

Given: , and A2 = λA + μI


So


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




[as cij = ai1b1j + ai2b2j + … + ainbnj]



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





But given, A2 = λA + μI


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




[as rij = aij + bij + cij],


And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal


Hence, λ + 0 = 4 λ = 4


And also, 2λ + μ = 7


Substituting the obtained value of λ in the above equation, we get


2(4) + μ = 7 8 + μ = 7 μ = – 1


Therefore, the value of λ and μ are 4 and – 1 respectively


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