If and , then

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

If $A = [\begin{array}{ccc} 2 & 1 & 3 \\ 4 & 5 & 1 \end{array}]$ and $B = [\begin{array}{cc} 2 & 3 \\ 4 & 2 \\ 1 & 5 \end{array}]$ , then

AB and BA both are not defined

only BA is defined

AB and BA both are defined

Only AB is defined

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Let A = [a_ij]_2×3, B = [b_ij]_3×2.

For, AB columns of A = 3 is equal to rows of B = 3. So, AB is defined.

For, BA columns of B = 2 is equal to rows of A = 2. So, BA is defined.

So, Both AB and BA are defined.