Compute `A^-1` for the matrix `A=[[2,3],[5,-2]]` and show that `A^-1=1/19A`.

If A=[(2,-1),(-1,2)] , then show that A^(2) -4A +3I=O .

If A = [(3, 1),(-1, 2)] show that A^2 - 5A + 7I = 0 .

If the matrix [[5-x, x+1],[2,4]] is singular, find x .

For what value of k, the matrix [[2-k, 3],[-5,1]] is not invertible ?

Show that the matrix A = [[4,1],[-2,3]] satisfy the equation A^(2) - 7A + 14l = O , where l is 2 xx 2 identity matrix and O is 2 xx 2 zero matrix. Using this equation , find A^(-1) .

Given a matrix A = [(2, -1),(4, 2)] Find matrix KA, where K = -1/2 .

If A=[(1,2),(3,4)] , find a matrix B such that AB=I .

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

If A = [(2,3),(3,10)],I=[(1,0),(0,1)] then show that (2I -A) (10I-A) = 9I .

For what value of a, [[2a, -1],[-8,3]] is a singular matrix ?