Question

if some one know this can that explain this to me

Answer 1

Hi there!

Given that A and B be two matrices such that:

• AB = B........ equation (1)

and,

• BA = A...........equation (2)

In the first equation, when the two matrices A and B are multiplied, we get the answer B , so here A is an identity matrix.
Because when we multiply a matrix with an identity matrix, we get the same matrix.

Similarly, in equation 2 we can see that when the two matrices are multiplied, we get the answer A so here B is an identity matrix.

Now,
To prove:

A² + B² = A + B
For this, we can conclude from the above two equations that both the matrices, A and B are identity matrices.
And the square of an indentity matrix is also an identity matrix.
i.e. A² = A
and,
B² = B
therefore,
A² + B² = A + B

Hence Proved!

Hope it helps!!✌