Show that
(i) `[(5,-1),(6,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(5,-1),(6,7)]`
(ii) `[(1,2,3),(0,1,0),(1,1,0)][(-1,1,0),(0,-1,1),(2,3,4)] ne [(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)]`

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)]

Find x and y, if 2[(1,3),(0,x)]+[(y,0),(1,2)]=[(5,6),(1,8)]

Find x, if [(x, -5, -1)][(1,0,2),(0,2,1),(2,0,3)][(x),(4),(1)]=O

Find |3A|,if A=[(1,0,1),(0,1,2),(0,0,4)]

Given A=[(1,1,1),(2,4,1),(2,3,1)], B=[(2,3),(3,4)]. Find P such that BPA= [(1,0,1),(0,1,0)]

Evaluate the determinants (i) {:[( 3,-1,-2),( 0,0,-1),( 3,-5,0) ]:} " " (ii) {:[( 3,-4,5),( 1,1,-2),(2,3,1) ]:} (iii) {:[( 0,1,2),(-1,0,-3),(-2,3,0)]:}" "(iv) {:[(2,-1,-2),(0,2,-1),(3,-5,0)]:}

Solve |( 0,0,7), (1,2,3), (0,8,2)|

If A=((1,1,-1),(2,0,3),(3,-1,2)),B=[(1,3),(0,2),(-1,4)] and C=[(1,2,3,-4),(2,0,-2,1)] prove that (AB)C=A(BC)

If A=[(1,2,3),(2,3,1)] and B=[(3,-1,3),(-1,0,2)] , then find 2A-B .

Show that ( -2,3,5) ( 1,2,3) (7,0,-1) are collinear