hey need help urgent questions

A, B, C are m × n matrices. Is it true that

a) A + B = B + A

b) (A + B) + C = A + (B + C)?

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- Mar 6th 2009, 06:24 PMsmmmcmatrices question
hey need help urgent questions

A, B, C are m × n matrices. Is it true that

a) A + B = B + A

b) (A + B) + C = A + (B + C)? - Mar 6th 2009, 06:27 PMProve It
- Mar 6th 2009, 06:30 PMsmmmc
ok thanks how bout this one

1)A and B are both m × n matrices. Are AB and BA defined and, if so, how many rows and

columns do they have?

2)The matrices A and B are 2 × 2 matrices, and O is the zero 2 × 2 matrix. Is the following

argument correct?

‘If AB = O, and A = O, then B = O’. - Mar 6th 2009, 06:33 PMProve It
No they're not.

If matrix A was m x n and matrix B was n x m, they both would be.

AB would be m x m and BA would be n x n.

In general, if you have two matrices, I'll call them X and Y, they can only be multiplied together (in the form XY, not YX) if the number of columns in X and the number of rows in Y are equal. XY will have the same number of rows as X and the same number of columns as Y.