A Note If elements of a row (or column) are multiplied with cofactors of any

A Note If elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero. For example, ∆ = a A + a A + a A = a (– ) + + a (– ) + + a (– ) + = (since R and R are identical) Similarly, we can try for other rows and columns. Example Find minors and cofactors of the elements of the determinant and verify that a A + a A + a A = Solution We have M = = – = – ; A = (– ) + (– ) = – M = = – – = – ; A = (– ) + (– ) = M = = – = ; A = (– ) + ( ) = M = – = – = – ; A = (– ) + (– ) = M = = – – = – ; A = (– ) + (– ) = – M = = + = ; A = (– ) + ( ) = – M = = – – = – ; A = (– ) + (– ) = – M = = – = – ; A = (– ) + (– ) = and M = = + = ; A = (– ) + ( ) = Now a = , a = – , a = ; A = – , A = , A = So a A + a A + a A = (– ) + (– ) ( ) + ( ) = – – + = DETERMINANTS EXERCISE . Write Minors and Cofactors of the elements of following determinants: .