Question

If A = \(\begin{bmatrix} 3 & 1 \\[0.3em]-1 &2 \\[0.3em]\end{bmatrix}\)show that A² - 5A + 7I₂ = 0.

Answer 1

For A²

For 5A

I₂ is an identity matrix of order 2 x 2,

Therefore,

To prove 

A² - 5A + 7I₂ = 0

Substituting the value from eq (i), (ii) and (iii)

Hence proved