please help me i have been stuck on this homework question for a very long time.

Question

Question 1: Identify the dimensions of P.

A.) 2 × 3

B.) 3 × 2

C.) 2 × 2

D.) 1 × 2

Question 2: Evaluate PQ if possible.

A.)

B.) Not possible

C.)

D.)

Question 3: Find P² if possible.

A.)

B.)

C.)

D.) Not possible

Please just give and only give explanation and solution.

Answer 1

It's 3 x 2;

# of rows is the first dimension..

3 by 2 times 2 by 3 = 3 by 3

2 * -1 + 0 * 2 = -2

2 * 0 + 0 * -2 = 0

2 * 2 + 0 * 3 = 4

4 * -1 + 5 * 2 = -4+10 = 6

4 * 0 + 5 * -2 = -10

4 * 2 + 5 * 3 = 8 + 15 = 23

1 * -1 + -1 * 2 = -1 + -2 = -3

1 * 0 + -1 * -2 = 2

1 * 2 + -1 * 3 = 2 + -3 = -1

Final Answer

-2 0 4

6 -10 23

-3 2 -1

so option 2

Finally, P^2 = P*P which is 2 by 3 times 2 by 3

NOT POSSIBLE

Answer 2

1) The answer is B), since an m x n matrix has m rows and n columns.

2) The multiplication is possible since the number of columns of A is equal to the number of rows of B. We also know that if you multiply an (a x b) matrix by a (b x c) matrix, the resulting matrix will have dimensions (a x c). In this case, since the first matrix is a (3 x 2) matrix and the second matrix is a (2 x 3) matrix, the matrix resulting from their multiplication will be a (3 x 3) matrix. Since the only matrix that is a 3 x 3 matrix is C), that is the correct answer.

3) Squaring a matrix (multiplying it by itself) is only possible if the number of rows and the number of columns are equal since matrix multiplication requires that the number of columns of the first matrix equals the number of rows of the second matrix. Since it is not possible, the answer is D).