If `A=[[1,0,1],[0,2,0],[1,-1,4]],A=B+C,B=B^(T)` and `C=-C^(T)`, then `C=`

If A=[[1,0],[0,1]],B=[[1,0],[0,-1]] and C=[[0,1],[1,0]] then show that A^(2)=B^(2)=C^(2)

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

If A=[[0,a,b],[-a,0,c],[-b,-c,0]] , find 1/2 (A+A\') and 1/2 (A-A\')

If A=[(-1,0,2),(3,1,4)], B=[(0,-2,5),(1,-3,1)] and C=[(1,-5,2),(6,0,-4)], then find (2A-3B+4C).

If A=[[1,2,3],[-1,0,2],[1,-3,1]], B=[[4,5,6],[-1,0,1],[2,1,2]], C=[[-1,-2,1],[-1,2,3],[-1,-2,2]] find A-2B+3C. Also verify that (A+B)+C=A+(B+C).

if A=[(1,2),(3,4):}],B=[{:(-1,0),(2,3):}]and C=[{:(1,-1),(0,1):}], then show that : (i) A(B+C)=AB+AC (ii) (A-B)C=AC-BC.

Let A+B+C=[[4,-10,1]],4A+2B+C=[[0,-1-3,2]] and 9A+3B+C=[[0,-22,1]] then find A

If A=[[0,a,b],[-a,0,c],[-b,-c,0]] find (1)/(2)(A+A') and (1)/(2)(A-A')

If A=[{:(1,2),(-1,3):}]B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}] a=4 and b=-2, then show that (i) (a+b)B=aB+bB (ii) a(C-A)=aC-aA (iii) (bA)^(T)=bA^(T)

If A=[(0,-1,2),(1,0,3),(-2,-3,0)], then A+2A^t equals (A) a (B) -A^t (C) A^t (D) 2A^2