If `A=[[4,3,2],[-1,2,0]],B=[[1,2],[-1,0],[1,-2]]`show that matrix AB is non singular.

Answer the following questions.If A=[[1,2],[3,2],[-1,0]] and B=[[,1,3,2],[4,-1,-3]] ,show that AB is singular matrix.

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

If A=[[1,2,2],[2,1,2],[2,2,1]] show that A^2-4A is a scalar matrix.

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

Answer the following questions.If A=[[1,2,3],[2,4,6],[1,2,3]] and B=[[1,-1,1],[-3,2,-1],[-2,1,0]] ,show that AB and BA are both singular matrices.

If A=[[1,2],[3,5]],B=[[0,4],[2,-1]] show that AB!=BA but |AB|=|A|.|B|

If A=[[-1,1,1],[2,3,0],[1,-3,1]],B=[[2,1,4],[3,0,2],[1,2,1]] State whether AB=BA ? Justify your answer.

Answer the following questions.If A=[[2,-4],[3,-2],[0,1]],B=[[1,-1,2],[-2,1,0]] ,show that (AB)^T=B^TA^T

Answer the following questions.If A=[[0,1],[1,0]],B=[[0,-1],[1,0]] ,show that (A+B).(A-B)!=A^2-B^2