For `2times2` matrices `A,B` and `I,` if `A+B=I` and `2A-2B=I`, then A equals
1) `[[(1)/(4),0],[0,(1)/(4)]] `
2) `[[(1)/(2),0],[0,(1)/(2)]]`
3) `[[(3)/(4),0],[0,(3)/(4)]],`
4) `[[1,0],[0,1]]`

In the structure of diamond, carbon atoms appear at a. 0, 0, 0 , and (1)/(2), (1)/(2), (1)/(2) b. (1)/(4), (1)/(4), (1)/4 , and (1)/(2), (1)/(2), (1)/(2) c. 0, 0, 0 , and (1)/(4), (1)/(4), (1)/(4) d. 0, 0, 0 , and (3)/(4), (3)/(4), (3)/(4)

If A[{:(3,-4),(1,1),(2,0):}] and B=[{:(2,1,2),(1,2,4):}] and B=[{:(4,1),(2,3),(1,2):}]

If A=[[1,2,3],[2,0,-2]],B=[[1,1,-1],[2,0,3],[3,-1,2]] and C=[[1,3],[0,2],[-1,4]] find A(BC).

If A=[[1,2,3],[0,1,0],[1,1,0]] and B=[[-1,1,0],[0,-1,1],[2,3,4]] show that AB!=BA

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

if A = [[3,9,0],[1,8,-2]] and B = [[4,0,2],[7,1,4]] find A+B and A-B?

If A=[[2,1,3],[4,1,0]] and B=[[1,-1],[0,2],[5,0]] find AB and BA.

If A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is (a) [(2, 2,-4 ),(2, 3, 4),(-4, 4, 2)] (b) [(2, 4,-5),( 0, 3, 7),(-3, 1, 2)] (c) [(4, 4,-8),( 4, 6, 8),(-8, 8, 4)] (d) [(1, 0 ,0 ),(0 ,1 ,0),( 0, 0, 1)]

For the matrices A and B , A=[[2 ,1 ,3 ] , [4 ,1 ,0 ]] , B=[[1 , -1] , [ 0, 2 ] , [ 5 , 0]] verify that (A B)^T=B^T\ A^T