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in Matrices by (26.9k points)
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If A = \(\begin{bmatrix} 2 & -1& 3 \\[0.3em] -4 & 5 &1 \\[0.3em] \end{bmatrix}\) and B = \(\begin{bmatrix} 2& 3 \\[0.3em] 4 & -2 \\[0.3em] 1 & 5 \end{bmatrix}\),then 

A. only AB is defined 

B. only BA is defined 

C. AB and BA both are defined 

D. AB and BA both are not defined

1 Answer

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by (27.3k points)
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Best answer

(C). AB and BA both are defined

As the matrices, 

A & B, both are defined, having orders as 2× 3 & 3 × 2, 

So multiplication of matrices is defined. (AB ≠ BA) 

Matrix multiplication is defined only if

Hence, 

AB and BA both are defined. 

Option (C) is the answer.

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