Given :

Matrix A is of order 2 2.

To show : A³ - 4A² + A = 0

Formula used :

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

A² and A³ are matrices of order 2 x 2.

A² = = =

A² =

A³ = = =

A³ =

4A² = 4 × =

4A² =

A³ - 4A² + A = + = =

A³ - 4A² + A = 0