Find minors and cofactors of the elements `a_11 ,a_21 `in the determinant ` Delta= {:|( a_11,a_12,a_13),( a_21,a_22,a_23),( a_31,a_32,a_33) |:}`

Find minors and cofactors of the elements of the determinant {:[( 2,-3,5),( 6,0,4),( 1,5,-7)]:} and verify that a_11 A_31+ a_12A_32+a_13A_33=0

Let S = {1,2,3}. Determine whether the functions f : S to S defined as below have inverses. Find f ^(-1), if it exists. (a) f = {(1,1), (2,2), (3,3)} (b) f = {(1,2), (2,1),(3,1)} (c ) f { (1,3), (2,3),(2,1)}

If Delta= [[ a_11 , a_12 , a_13],[a_21 , a_22 , a_23],[a_31 , a_32 , a_33 ]] and A_ij is the cofactor of a_ij then the value of Delta is given by

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]