`A=[[1,-2,3],[1,4,1],[1,-3,2]] Then |A|=`

If A = [[-1, 2 ,3],[-1, 0, 2],[1, -3, 1]] and B = [[4,5,6],[-1, 0, 1], [2,1,2]], find 4A-3B

Given two matrices A and B, A = [(1,-2,3),(1,4,1),(1,-3,2)] , B = [(11,-5,-14),(-1,-1,2),(-7,1,6)] Find AB and use this result to solve the following system of equations : x - 2y + 3z = 6, x + 4y + z = 12, x-3y + 2z = 1

If A=[[0 ,1 ,3],[ 1, 2,x],[2, 3, 1]] and A^(-1)=[[1//2,-4 ,5//2],[-1//2, 3,-3//2],[ 1//2,y,1//2]] ,find x ,\ y .

4.If A= [[2,3,1],[-1,2,3],[1,0,2]] . Prove that (A')^-1 = (A^-1)'

Statement 1: A=[(4,0,4),(2,2,2), (1,2,1)] B^(-1)=[(1,3,3),(1,4,3),(1,3,4)] . Then (A B)^(-1) does not exist. Statement 2: Since |A|=0,(A B)^(-1)=B^(-1)A^(-1) is meaning-less.

find the rank of matrix A=[[2,-1,-2,-4],[1,3,-1,-1],[3,1,-1,-1],[6,3,0,-7]]

If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[5//2,-3//2,1//2]] then

If A=[[3, -1, 4], [2, 3, 1]], B=[[1, 3, 4], [2, 1, 0], [-3, 2, 3]] find AB

If A=[[2,3],[1,-4]] and B=[[1,-2],[-1,3]] , then verify that (A B)^(-1)=B^(-1)A^(-1)

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).