My question is from Matrices grade 12 no links pls: â ‹Let A=01-10, Find x - Maths - Matrices

Question

My question is from Matrices grade 12 no links pls:

â€‹Let A = 0 1 - 1 0 ,   Find   x
  and   y   such   that   xI   +
  y A 2 = A

Neha Sethi · Accepted Answer

Dear student
Given: A=01-10Consider,xI+yA2=Ax1001+y01-102=01-10⇒x00x+0y-y02=01-10⇒xy-yx2=01-10⇒xy-yxxy-yx=01-10⇒x2-y2xy+xy-xy-xy-y2+x2=01-10⇒x2-y22xy-2xyx2-y2=01-10On comparing , we getx2-y2=0 and 2xy=1⇒x2=y2 and xy=12⇒x=12y12y2=y2⇒14y2=y2⇒4y4=1⇒y4=14On solving we gety=±12,±i12   Case I, When y=12So, x=12×12=12Case II, When y=-12So, x=12×-12=-12

Case III: When y=i2then , x=12×i2=22i=12i×ii=i-2  as i2=-1Case IV: When y=-i2then , x=12×-i2=-22i=-12i×ii=-i-2=i2  as i2=-1
Regards

My question is from Matrices grade 12 ... no links pls: ​Let A = 0 1 - 1 0 , Find x and y such that xI + y A 2 = A .

My question is from Matrices grade 12 ... no links pls:

Let $A = [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}], Find x and y such that {(xI + y A)}^{2} = A .$