Given : A = \(\begin{bmatrix}
3 &2 \\[0.3em]
1&1 \\[0.3em]
\end{bmatrix}\), 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 x b and B is a matrix of order c x d ,then matrix AB exists and is of order a x d ,
if and only if b = c
A2 is a matrix of order 2 x 2
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