# If find x and y such that A2 + xI = yA.

Given : A2 + xI = yA.

A is a matrix of order 2 x 2

To find : x and y

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 = =

A2 =

xI = =

xI =

A2 + xI = + = =

A2 + xI =

yA = y =

yA =

It is given that A2 + xI = yA,

=

Equating similar terms in the given matrices,

16 + x = 3y and 8 = y,

hence y = 8

Substituting y = 8 in equation 16 + x = 3y

16 + x = 3 × 8 = 24

16 + x = 24

x = 24 – 16 = 8

x = 8

x = 8, y = 8

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