If `A=[[2,-3],[5,-4],[-6,1]],B=[[2,1],[4,-1],[-3,3]] and C=[[1,2],[-1,4],[-2,3]]`,show that`(A-C)^T=A^T-C^T`

If A=[[2,-3],[5,-4],[-6,1]],B=[[2,1],[4,-1],[-3,3]] and C=[[1,2],[-1,4],[-2,3]] ,show that (A+B)^T=A^T+B^T

If A=[[2,-3],[5,-4],[-6,1]],B=[[-1,2],[2,2],[0,3]] and C=[[4,3],[-1,4],[-2,1]] show that: A+B=B+A

If A=[[1,2,-3],[5,0,2],[1,-1,1]],B=[[3,-1,2],[4,2,5],[2,0,3]] and C=[[4,1,2],[0,3,2],[0,-2,3]] verify that A(B+C)=AB+AC

If A=[[2,-1],[3,-2],[4,1]] and B=[[0,3,-4],[2,-1,1]] ,verify that (BA)^T=A^TB^T

If A=[[2,-1],[3,-2],[4,1]] and B=[[0,3,-4],[2,-1,1]] ,verify that (AB)^T=B^TA^T

If A=[[-1,2,1],[-3,2,-3]] and B=[[2,1],[-3,2],[-1,3]] , prove that (A+B^T)^T=A^T+B

If A=[[1,0,1],[3,1,2]],B=[[2,1,-4],[3,5,-2]], and C=[[0,2,3],[-1,-1,0]], verify that [A+2B+3C]^T=A^T+2B^T+3C^T

If A=[[3,4],[-4,3]] and B=[[2,1],[-1,2]] show that (A+B) . (A-B)=A^2-B^2

If A=[[1,2,-5],[2,-3,4],[-5,4,9]] ,prove that (A)^T=A

If A=[[5,-3],[4,-3],[-2,1]] ,prove that (A^T)^T=A