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 c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

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