Given : A = \( \begin{bmatrix} 1& -1 \\[0.3em] 2 & -1 \\[0.3em] \end{bmatrix}\) , B = \( \begin{bmatrix} a& -1 \\[0.3em] b & -1 \\[0.3em] \end{bmatrix}\)
(A + B)2 = (A2 + B2)
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
It is given that (A + B)2 = (A2 + B2)
Equating similar terms in the given matrices we get,
2 – 2a = -a + 1 and -2b = -b + 1 2 – 1
= -a + 2a and -2b + b = 1
1 = a and -b = 1
a = 1 and b = -1