If `A = [(2,0,1),(0,-3,0),(0,0,4)]`, prove that.` A^(3) - 3A^(2) - 10A + 24I = 0` where 0 is zero matrix of order `3 xx 3`

If A=[[1,0,20,2,12,0,3]], prove that A^(3)-6A^(2)+7A+2I=0

If A=[[1,-3,22,0,-11,2,3]], then show that AA^(3)-4A^(2)-3A+11I=0 where O and I are null and identity matrix of order 3 respectively.

Let A = ((1,-1,0),(0,1,-1),(0,0,1))andB=7A^(20)-20A^(7)+2I, where I is an identity matrix of order 3 xx 3 if B = [b_(ij)] then b_(13) is equal to __________ .

Let A=[(2,0,7),(0,1,0),(1,-2,1)] and B=[(-k,14k,7k),(0,1,0),(k,-4k,-2k)] . If AB=I , where I is an identity matrix of order 3, then the sum of all elements of matrix B is equal to

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

If A=((1,0,0),(0,2,1),(1,0,3)) then (A-I)(A-2I)(A-3I)=

Consider a matrix A=[(0,1,2),(0,-3,0),(1,1,1)]. If 6A^(-1)=aA^(2)+bA+cI , where a, b, c in and I is an identity matrix, then a+2b+3c is equal to

If A=[(1,0),(0,3)] and B=[(2,0),(0,1)] then show AB =BA =[(2,0),(0,3)]