(det ( ) ( ABC C B A . If ( AB − = and A − = , then B − = ( ) ( ) ( ) ( ) - - Applications of Matrices and Determinants . If A A T − is symmetric, then A = ( ) A − ( ) ( A T ( ) A T ( ) ( A − . If A is a non-singular matrix such that A − = − , then ( A T − = ( ) − ( ) ( ) − ( ) .
If A and A T = − , then the value of x is ( ) − ( ) − ( ) ( ) . If A = and AB I , then B = ( ) cos A ( ) cos A T ( ) (cos θ I ( ) sin A . If A = − θ and A adj = , then k = ( ) ( ) sin θ ( ) cos θ ( ) . If A = be such that λ A − = , then λ is ( ) ( ) ( ) ( ) .
If adj A = and adj B = then adj ( AB is ( ) − ( ) − ( ) − ( ) − . The rank of the matrix is ( ) ( ) ( ) ( ) . If x y e x y e m m m ∆= ∆= ∆= then the values of x and y are respectively, ( ) e e / / D D D D