If and then find λ so that A2 = 5A + λI.

Given: , and


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 eqn(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, and


So the value of λ so that is – 7


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