Let A be a matrix such that A* `[(1 ,2) ,(0 ,3)]` is a scalar matrix and |3A|=108 .Then `A^(2)` equals

Scalar matrix and identity matrix

Let A be a matrix of order 3 such that A^(2)=3A-2I where, I is an identify matrix of order 3. If A^(5)=alphaa+betaI , then alphabeta is equal to

Let A be a matrix such that adj (adj A)= [(5,2,1),(3,1,0),(2,2,1)] then the value of

Let A=[(-1,2,-3),(-2,0,3),(3,-3,1)] be a matrix, then |A|adj(A^(-1)) is equal to

If P = [{:(3, 0), (0, lambda):}] is scalar matrix then lambda = ____.

Let A=[(-1, 2, -3),(-2,0,3),(3,-3, 1)] be a matrix, then |a| adj(A^(-1)) is equal to

If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equal to

If A is any 2 xx matrix such that [{:(1,2),(0,3):}]A=[{:(-1,0),(6,3):}] then what is A equal to ?

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .