Question

a <b then a^2< b^2 is true or false
Plz answer fast​

Answer 1

Answer:

Thus if (A−B)(A+B)=A2−B2 then AB−BA=O, the zero matrix. Equivalently, AB=BA. Note that matrix multiplication is not commutative, namely, AB≠BA in general. Thus we can disprove the statement if we find matrices A and B such that AB≠BA.

Step-by-step explanation:

Solution.

Let us calculate (A−B)(A+B) as follows using the fact that the matrix product is distributive.

(A−B)(A+B)=A(A+B)−B(A+B)

=A^2+AB−BA−B^2

=A^2−B^2+(AB−BA).

Thus if (A−B)(A+B)=A^2−B^2 then

AB−BA=O, the zero matrix. Equivalently,

AB=BA.

Note that matrix multiplication is not commutative, namely, AB≠BA in general.

Note that matrix multiplication is not commutative, namely, AB≠BA in general.Thus we can disprove the statement if we find matrices A and B such that AB≠BA.