a a – a a a ... ( ) A Note We shall apply all four steps together. Expansion along second row ( R ) | A | = Expanding along R , we get | A | = (– ) (– ) (– ) = – a ( a a – a a ) + a ( a a – a a ) – a ( a a – a a ) | A | = – a a a + a a a + a a a – a a a – a a a + a a a = a a a – a a a – a a a + a a a + a a a – a a a ... ( ) Expansion along first Column (C ) | A | = By expanding along C , we get | A | = (– ) ( ) (– ) = a ( a a – a a ) – a ( a a – a a ) + a ( a a – a a ) | A | = a a a – a a a – a a a + a a a + a a a – a a a = a a a – a a a – a a a + a a a + a a a – a a a ...
( ) Clearly, values of |A| in ( ), ( ) and ( ) are