Given:
The product of matrix is given.
To determine the dimension of product of the matrix,
[tex]\lbrack A\rbrack_{m\times n}\cdot\lbrack B\rbrack_{n\times k}=\lbrack AB\rbrack_{m\times k}[/tex]a)
[tex]\lbrack X\rbrack_{1\times2}\cdot\lbrack Y\rbrack_{2\times3}=\lbrack XY\rbrack_{1\times3}[/tex]b) The matrix multiplication is defined only if the number of columns of first matrix is equal to the number of rows in the second matrix.
Here, number of column in first matrix is 3 and number of rows in second matrix is 2. which is not equal.
[tex]\lbrack X\rbrack_{2\times3}\cdot\lbrack Y\rbrack_{2\times3}=\text{Not defined}[/tex]c)
[tex]\begin{gathered} \lbrack X\rbrack_{3\times2}\cdot\lbrack Y\rbrack_{3\times2}=\text{Not defined} \\ Since,\text{Number of columns}\ne\text{Number of rows} \end{gathered}[/tex]