If A = [(1,2)(2,1)], and f(x) = x^2 – 2x - 3, show that f(A) = 0. ​

Question

If A =\( \begin{bmatrix} 1 &2 \\[0.3em] 2 & 1 \end{bmatrix}\), and f(x) = x² – 2x - 3, show that f(A) = 0.

Answer 1

Given,

 A =\( \begin{bmatrix} 1 &2 \\[0.3em] 2 & 1 \end{bmatrix}\) and

f(x) = x² - 2x - 3

To show that,

f(A) = 0

Substitute x = A in f(x), we get

f(A) = A² - 2A - 3I ....(i)

I is an identity matrix,

So,