linear algebra expect answers to be typing answer hand writi

?linear algebra?

expect answers to be typing answer, hand writing is fine but please be clear.

1.

2.

Solution

1.

AB is invertible

Hence

det(AB) is non zero

BUt, A,B are square matrices

SO, det(AB)=det(A)det(B)

Hence, det(A) and det(B) are also non zero

Hence, A and B are also invertible

2.

CA=I

Hence

det(CA)=1

ie CA is invertible.

C,A are square matrices

Hence, det(CA)=det(C)det(A)

Hence, det(A) is non zero

Ie A is invertible

Hence, nul(A)={0}

HEnce, Ax=0 has only trivial solution.