Verify that `A(B+C)=AB+AC` in each of the following matrices `A=[[4,-2],[2,3]],B=[[-1,1],[3,-2]]`and `C=[[4,1],[2,-1]]`

Verify that A(B+C)=AB+AC in each of the following matrices A=[[1,-1,3],[2,3,2]],B=[[1,0],[-2,3],[4,3]] and C=[[1,2],[-2,0],[4,-3]]

Verify that A(BC)=(AB)C in each of the following: A=[[2,4,3],[-1,3,2]],B=[[2,-2],[3,3],[-1,1]] and C=[[3,1],[1,3]]

Verify that A(BC)=(AB)C in each of the following: A=[[1,0,1],[2,3,0],[0,4,5]],B=[[2,-2],[-1,1],[0,3]] and C=[[3,2,-1],[2,0,-2]]

Write the transpose of each of the following matrices: B=[[4,6,3],[1,0,4],[0,2,3]]

Find k,if the following matrices are singular: [[k-1,2,3],[3,1,2],[1,-2,4]]

Apply the given elementary transformation on each of the following matrices: A = [[1,2,-1],[0,1,3]] , 2C_2 , B = [[1,0,2],[2,4,5]] , -3R_1 . Find the addition of the new matrices.

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

Answer the following questions. If A=[[2,1],[0,3]],B=[[1,2],[3,-2]] ,verify that |AB|=|A||B|

Apply the given elementary transformation on each of the following matrices: A = [ [5,4] ,[1,3] ] C_1 harr C_2 , B = [[3,1],[4,5]] , R_1 harr R_2 . What do you observe?

Apply the given elementary transformation on each of the following matrices: A = [[1,-1,3],[2,1,0],[3,3,1]] , Apply 3R_3 and then C_3+2C_2