Prove the following A(rB)= r(AB)= (rA)B where r and s are real numbers and A and B are matrices

Prove the following A(rB)= r(AB)= (rA)B where r and s are real numbers and A and B are matrices

asked 2021-02-14
Prove the following
A(rB)= r(AB)= (rA)B
where r and s are real numbers and A and B are matrices

Answers (1)

Given that A and B are matrices and r is a real number.
Let us consider the matrix A is of order
and let us consider the matrix B is of order
Hence the result for A(rB) will be of order
Hence the result for (rA)B will be of order
Since the results for the above three is of order
Therefore A(rB)= r(AB)= (rA)B

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