For the matrix a = [ ll 3&1 1&2 ], find the numbers a and b such that A2 + aA + bI = O.

We have A2 = A.A =

Since A2 + aA + bI =


So A2 + aA + bI =


Hence 10+3a+b = 0 …(i)


5+a = 0 …(ii)


5+2a+b = 0 …(iii)


From (ii) a = -5


Putting a in (iii) we get b = 5


So a = -5 and b = 5 satisfy the equation.


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