Show that ` A=[[2,1,2],[1,0,1],[2,2,1]]` is non singular and find `A^(-1)`.

Show that [[1,1],[0,1]]^2 = [[1,3],[0,1]]

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and hence find A^(-1)

For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singular?

The matrix [(2,lambda,-4),(-1,3,4),(1,-2,-3)] is non singular , if :

If the matrix [[5x,2],[-10 ,1]] is singular, find the value of x .

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

Find the value of x for which the matrix A=[(2//x,-1,2),(1,x,2x^(2)),(1,1//x,2)] is singular.

If A=[[1,-1, 1],[ 2,-1, 0],[ 1, 0, 0]] , show that A^(-1)=A^2 .

Find the rank of matrix A= [[1,2,-1,0],[0,1,3,1],[2,5,1,2]]

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