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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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