Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and `11 - n` columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB

Question

Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and `11 - n` columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB

Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and `11 - n` columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB and BA are of order `8 xx 8` and `3 xx 13`, respectively (C) `AB=BA` (D) None of these

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

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 (20, we get `n=3` and `m=8`. Hence, A has order `8xx8` has order `8xx8`. Hence, both AB and BA are square matrices.