A = [(3, 1) (-1, 2)] , prove that A^2 – 5A + 7I = 0, where I is unit matrix of order 2.

Question

If A =\(\begin{vmatrix}3&1\\-1&2\end{vmatrix}\), prove that A² – 5A + 7I = 0

where I is unit matrix of order 2.

A = [(3, 1) (-1, 2)]  

Answer 1

A² – 5A + 7I = 0 = A.A – 5A + 7I = 0