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in Trigonometry by (41.5k points)

Matrix A has 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 matrices

(B) AB and BA are of order 8 × 8 and 3 × 13, respectively

(C) AB = BA

(D) None of these 

1 Answer

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Answer is (A) AB and BA are square matrices

O(A) = m × (n + 5) and O(B) = m × (11 - n)

AB exists ⇒ n + 5 = m ⇒ m - n = 5 (1)

BA exists ⇒ 11 - n = m ⇒ m + n = 11 (2)

Solving Eqs. (1) and (2), we have

m = 8 and n = 3

Therefore, O(A) = 8 × 8 and O(B) = 8 × 8

Therefore, AB and BA both are square matrices of order 8 × 8.

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