If `A={:((4,2),(-1,1))and I={:((1,0),(0,1)),` prove that,
`(A-2I)(A-3I)={:((0,0),(0,0)).`

If I={:((1,0),(0,1)):} and E={:((0,1),(0,0)):} prove that, (2I+3E)^(3)=8I+36E.

If A={:[(1,0),(-1,7)] and I={:[(1,0),(0,1)] , then find k so that A^(2)=8A+kI

If A={:[(a,b),(c,d)] and I={:[(1,0),(0,1)] Show that, A^(2)-(a+d)A=(bc-ad)I .

If A={:[(0,-1),(1,0)]:} and B={:[(0,i),(i,0)]:} , then

If A={:((1,4),(2,3)), show that, A^(2)-4A-5I=0 where I={:((1,0),(0,1))and 0={:((0,0),(0,0)).

If A=[(1,0,2),(0,2,1),(2,0,3)] , prove that A^(3)-6A^(2)+7A+2I=0

If A = ((3,1),(-1,2)), I = ((1,0),(0,1)) and O = ((0,0),(0,0)) show that, A^(2) - 5A + 7I = O . Hence find A^(-1) .

Verify that the matrix equation A^(2)-4A+3I = 0 is satisfied by the matrix A={:[(2,-1),(-1,2)]," where " I={:[(1,0),(0,1)]and 0={:[(0,0),(0,0)]. Hence obtain A^(-1).

If A={:[(2,-1),(3,2)]:} and B={:[(0,4),(-1,7)]:}, find 3A^(2)-2B+I

If A'=[(3,4),(-1,2),(0,1)] and B=[(-1,2,1),(1,2,3)] , then verify that (i) (A+B)' =A'+B', (ii) (A-B)'=A'-B'