If A – 1 = and , find (AB) – 1.(CBSE 2012)

Question

If A &ndash; 1 =  and , find (AB) &ndash; 1.(CBSE 2012)

Philoid · Accepted Answer

A &ndash; 1 =  B =

|B| = 1(3 &ndash; 0) &ndash; 2( &ndash; 1 &ndash; 0) &ndash; 2(2 &ndash; 0)

= 3 + 2 &ndash; 4

|B| = 1

Now, B &ndash; 1 =

Cofactors of B are:

C11 = &ndash; 3 C21 = 2 C31 = 6

C12 = 1 C22 = 1 C32 = 2

C13 = 2 C23 = 2 C33 = 5

adj B =

=

So, adj B =

Now, B &ndash; 1 =

(AB) &ndash; 1 = B &ndash; 1 A &ndash; 1

=

Hence, =

If A ^{– 1} = and , find (AB) ^{– 1}.(CBSE 2012)