Select all statements below which are true for all invertible n×nn×n matrices aa and bb a. (ab)−1=a−1b−1(ab)−1=a−1b−1 b. aba−1=baba−1=b c. (in+a)(in+a−1)=2in+a+a−1(in+a)(in+a −1)=2in+a+a−1 d. a2b7a2b7 is invertible e. a+ba+b is invertible f. (a+b)(a−b)=a2−b2(a+b)(a−b)=a2−b2

The statements that are correct are:

c)

d) is invertible.

e) is invertible.

Step-by-step explanation:

We are given that:

a and b are invertible n×n matrices.

We have to tell which of the following statements are true.

a)

This statement is false.

Since:

and it may not be equal to the term

b)

This expression could also be written as:

Since on Post multiplying by a on both the sides.

But here we don't know whether the matrices are commutative or not.

Hence, the statement is false.

c)

This statement is true.

since,

where in denote the identity matrix.

and we know that:

d)

is invertible.

This statement is true.

Since we know that prodct of invertible matrices is also invertible.

As is invertible so is .

Also is invertible so is .

Hence Product of   and   is also invertible.

i.e. is invertible.

e)

is invertible.

This statement is true as sum of two invertible matrices is invertible.

f)

This statement is false.

Since,

Now as we are not given that:

Hence, we could not say that:

hello, there is a new name in town and that's the human spider!

answer: d.) the total number of protons and neutrons is 15

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~

your friendly neighborhood human spider! .