Matrix Properties

If A is a 5×8 matrix and B is a 8×6 matrix, and Z is a 6 × 5 zero matrix, which of the following statements is true?

• A + Z = A

• AB = BA

• BZ = Z

• ZA is a 6 × 8 zero matrix.

• cannot be determined

• The same as the second column of C

• The sum of the first and second columns of C

• The sum of the second and fourth columns of C

• The same as the third row of D

• The sum of the first and the third columns of C

If A is a 2 × 3 matrix and C is a 2 × 2 matrix, and AB = C, what size is B?

• 2 × 2

• 2 × 3

• 3 × 2

• None of the choices given

• There is no matrix B for which this canhappen.

• A

• B

Calculator allowed

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True or False:

A•B is the same as B•A, for any matrices A and B.

• TRUE

• FALSE

Which of the following is NOT a property of matrix operations?

• A + B = B + A 

• AB = BA 

• (AB)C = A(BC)

• (A + B) + C = A + (B + C)

True or False:

A – B is the same as B – A, for any matrices A and B.

• TRUE

• FALSE

A(n) ____________ is a rectangular arrangement of numbers into rows and columns.

• matrix

• square

• identity

• scalar