If `A= [[3,1,1],[1,3,1],[1,1,3]]`, then show that `|3A| = 27 |A|`.

If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

If A = [[1,2,3],[3,-2,1],[4,2,1]] , then show that A^3 - 23A - 40I = O

If A= [[1,1,1],[1,1,1],[1,1,1]] then a. A^(3) = 9 A b. A^(3) = 27 A c. A + A = A^(2) d. A^(-1) does not exist

If A = [[1,3,3],[1,4,3],[1,3,4]] , then verify that A. adj A = |A|I. Also find A^-1 .

For the matrix A = [[1,1,1],[1,2,-3],[2,-1,3]] , show that A^3 - 6A^2 + 5A + 11I = 0 . Hence find A^-1 .

If A = [[1,1,1],[1,1,1],[1,1,1]] , prove that A^n = [[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)]], n in N

If A = {:[(1,2,3),(3,-2,1),(4,2,1)] , then show that : A^2 - 23 A - 40 I ne O

For the matrix A = [[1,1,1],[1,2,-3],[2,-1,3]] Show that A^3-6A^2+5A+11I=O Hence, find A^-1

If A = {:[(3,1,-1),(0,1,2)] , then show that AA' is a symmetric matrix.

If A = {:[(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1)] , then show that (A +B) = A'+B'