Question

A matrix A has m rows and n+5 columns .Another matrix B has m rows at 11-n columns . If both AB and BA exists then prove that AB Aand BA are square matrices

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER

If both AB and BA exist, then the number of columns of A is equal to the number of rows of B. Therefore,

n+5=m ....... (1)

And the number of columns of B is equal to the number of rows of A. Therefore,

11−n=m ...... (2)

Solving (1) and (2), we get n=3 and m=8. Hence, A has order 8×8 and B has order 8×8. Hence, both AB are BA are square matrices.

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