Verify A (adj A) = ( adj A) A= |A| I in Excercises 3 and 4 ` {:[( 2,3),(-4,-6) ]:} `

Find adj A for A = {:[( 2,3),( 1,4) ]:}

|{:(1,3,5),(2,4,3),(4,6,7):}|

Let's verify (-2) xx (-3) = 6

|{:(2,3,4),(3,4,5),(4,5,6):}|=0

|{:(2,3,4),(5,6,1),(3,2,3):}|

If A = [(a,b),(c,d)] show that, (i) adj (adj.A) = A (ii). (A^(-1))^(-1) = A .

If A=[(5a,-b),(3, 2)] and A adj A=A A^T , then 5a+b is equal to: (1) -1 (2) 5 (3) 4 (4) 13

Verify that the area of the triangle with vertices (6,2), (-3,4) and (4,-3) remains unaltered under the translation of axis when the origin is shifted to the point (2,-1).

Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt(k),1,-2k),(-2sqrt(k),2k,-1)] and B=[(0,2k-1,sqrt(k)),(1-2k,0,2sqrt(k)),(-sqrt(k),-2sqrt(k),0)] . If det (adj A) + det (adj B) =10^(6) , then [k] is equal to ______ . [Note : adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k .]

Verify whether 2x ^(4) - 6x ^(3) + 3x ^(2) + 3x -2 is divisible by x ^(2) - 3x +2 or not ? How can you verify using Factor Theorem ?