If `A = [[0,1],[0,0]]`, I is the unit null matrix of order 2 and a,b are arbitrary constants, then `(aI+bA)^2` is equal to

If {:A=[(0,1),(1,0)]:} ,I is the unit matrix of order 2 and a, b are arbitray constants, then (aI +bA)^2 is equal to

If {:A=[(0,1),(1,0)]:} ,I is the unit matrix of order 2 and a, b are arbitray constants, then (aI +bA)^2 is equal to

If A = [(1,0,0),(0,1,0),(a,b,-1)] and I is the unit matrix of order 3, then A^(2) + 2A^(4) + 4A^(6) is equal to a)7 A^(8) b)7 A^(7) c)8I d)6I

If A is a matrix of order 5xx2 and B is a matrix of order 2xx5 , then the order of matrix (BA)^T is equal to :

If A is a matrix of order 3xx2 and B is a matrix of order 2xx3 , then the order of matrix (BA)^T is equal to :

If A=[(1, 0,0),(0,1,0),(a,b,-1)] and I is the unit matrix of order 3, then A^(2)+2A^(4)+4A^(6) is equal to

Let A=[[0,1],[0,0]] , prove that: (aI+bA)^n = a^(n-1) bA , where I is the unit matrix of order 2 and n is a positive integer.

If A is a square matrix and I is the unit matrix of the same order as A, then A.I =

If A is an idempotent matrix satisfying,(I-0.4A)^(-1)=I-alpha A, where I is the unit matrix of the name order as that of A, then th value of |9 alpha| is equal to

If A=[(i,0),(0,-i)],B=[(0,-1),(1,0)] and C=[(0,i),(i,0)] and I is the unit matrix of order 2, then show that (i) A^(2)=B^(2)=C^(2)=-I (ii) AB=-BA=-C .