If A = [0&-1 1&0], then which one of the following statements is not correct ?

Question

If A = [0&-1 1&0], then which one of the following statements is not correct ? (A) A4 - I = A2 +I (B) A3 - I = A(A - I) (C) A2 + I = A(A2 - I) (D) A3 + I = A(A - I)

Tardigrade Admin · Accepted Answer

Given that A = [0&-1 1&0] A2 = [-1&0 0&-1] ⇒ A2 = -I A3 = [0&1 -1&0] A4 = [1&0 0&1] = I A2 +I = A3-A -I + I = A3-A A3 ≠ A

Q. If A = $[01 - 1 0]$ , then which one of the following statements is not correct ?

$A^{4} - I = A^{2} + I$

$A^{3} - I = A (A - I)$

$A^{2} + I = A (A^{2} - I)$

$A^{3} + I = A (A - I)$

Given that
$A = [01 - 1 0]$
$A^{2} = [- 1 0 0 - 1] \Rightarrow A^{2} = - I$
$A^{3} = [0 - 1 10]$
$A^{4} = [1001] = I$
$A^{2} + I = A^{3} - A$
$- I + I = A^{3} - A$
$A^{3} \neq = A$

Q. If A = [01​−10​], then which one of the following statements is not correct ?

A4−I=A2+I

A3−I=A(A−I)

A2+I=A(A2−I)

A3+I=A(A−I)