# If find the value of a and b such that A2 + aA + bI = O.

Given : A2 + aA + bI = O

A is a matrix of order 2 x 2

To find : a and b

Formula used : Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj

If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c

A2 is a matrix of order 2 x 2

A2 = = = A2 = aA = a = bI = b = bI = A2 + aA + bI = + + = A2 + aA + bI = It is given that A2 + aA + bI = 0 = Equating similar terms in the matrices,we get

4 + a = 0 and 3 + a + b = 0

a = 0 – 4 = -4

a = -4

substituting a = -4 in 3 + a + b = 0

3 – 4 + b = 0

-1 + b = 0

b = 0 + 1 = 1

b = 1

a = -4 and b = 1

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