Given : A² = kA – 2I.

Matrix A is of order 2 2.

To find : k

Formula used :

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

A² is a matrix of order 2 x 2.

A² = = =

A² =

kA = k × =

kA – 2I = =

It is the given that A² = kA – 2I

=

Equating like terms,

3k – 2 = 1

3k = 1 + 2 = 3

3k = 3

k = = 1

k = 1