if `A=[[0, 1],[ 1, 0]],t h e nA^4=`

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: IfA=[[a,1],[ 0,a]],t h e nA^n=[[a^n,n a^(n-1)],[0,a^n]] for every positive integer n.

the inverse of [[1,a, b],[0,x,0],[ 0, 0, 1]] i s[[1,-a,-b],[0 ,1 ,0],[ 0, 0, 1]] t h e n x=

If A_1=[(0, 0, 0, 1), (0, 0, 1, 0), (0, 1, 0, 0), (1, 0, 0, 0)],A_2=[(0, 0, 0,i),(0, 0,-i, 0), (0,i,0, 0),(-i,0, 0, 0)],t h e nA_i A_k+A_k A_i is equal to a. 2Iifi=k b. Oifi!=k c. 2lifi!=k d. O always

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

If [1 4 2 0]=[x y^2z0],y<0t h e nx-y+z=

If A_1=[0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0],A_2=[0 0 0i0 0-i0 0i0 0-i0 0 0],t h e nA_i A_k+A_k A_i is equal to 2lifi=k b. Oifi!=k c. 2lifi!=k d. O always

If [1 4 2 0]=[x y^2z0],y<0t h e nx-y+z= 5 (b) 2 (c) 1 (d) -3

Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statement 2; |A|=0,t h e nA^(-1) does not exist.

Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statement 2; |A|=0,t h e nA^(-1) does not exist.