`|[1+a,1,1],[1,1+a,1],[1,1,1+a]|=a^3+3a^2`

The ranks of the matrices in descending order A= [[1, 4, -1],[2, 3, 0],[0, 1, 2]] B= [[1, 1, 1],[1,1,1],[1,1,1]] C= [[1,2, 3],[2,3, 4],[ 0, 1, 2]]

Prove that |[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3

If A=([1,2,1],[0,1,-1],[3,-1,1]) then A^(3)-3A^(2)-A-9=

Verify that (AB)' = B 'A ' in A=[[1,2,1],[3,2,1]] and B=[[3,1],[1,1],[2,1]]

Consider the matrix A=[[2,1,3],[2,3,1],[1,1,1]] B=[[-1,2,3],[-2,3,1],[-1,1,1]] Find A+B

Show that [[1,2,3],[0,1,0],[1,1,0]] [[-1,1,0],[0,-1,1],[2,3,4]] ne [[-1,1,0],[0,-1,1],[2,3,4]][[1,2,3],[0,1,0],[1,1,0]]

Find the rank of A=[[-2,-1,-3,-1],[1,2,3,-1],[1,0,1,1],[0,1,1,-1]]

Let A= [{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B= [{:(,2,-1,-1),(,-1,2,-1),(,-1,-1,2):}] and C=3A+7B

Let A= [{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B= [{:(,2,-1,-1),(,-1,2,-1),(,-1,-1,2):}] and C=3A+7B

Find the rank of A=[[1,1,-1,1],[1,3,2,1],[2,0,3,2],[3,3,3,3]]