Question

iF A and B are invertible martrices of the same order,then prove that​

Answer 1

Answer

We know that if A.B =I then it means B is inverse of matrix A where I is an identity matrix.

If, we can prove that (AB).B^−1 A^−1 =I then it means that B^−1 A^−1 is inverse of AB.

In other words proving (AB).B^−1 A^−1 =I

⇒(AB)^−1=B^−1 A^−1

Lets simplify AB.B^−1 A^−1

⇒AIA^−1 =AA^−1 =I {AI=A and AA^−1 =I}

Therefore, from above equation, we can say that B−1A−1 is inverse of AB

⇒(AB)^−1=B^−1 A^−1

which is the desired equation.

Answer 2

Answer:

$\huge {\mathbb{\brown{Hello!!}}}$

Step-by-step explanation:

Now AB = BA = I since B is the inverse of matrix A. ... This proves B = C, or B and C are the same matrices. Theorem 2: If A and B are matrices of the same order and are invertible, then (AB)-1 = B-1 A-1.!

Thanks!