Video Transcript
Given that matrix 𝐴 equals five, one, two, negative three, negative four, negative three and matrix 𝐵 equals one, negative two, five, negative four, determine 𝐴𝐵 if possible.
In order to answer this question, we firstly need to recall when matrix multiplication is defined. In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix. We can multiply a matrix with order 𝑚 by 𝑛 by another matrix of order 𝑛 by 𝑘, and this results in an 𝑚 by 𝑘 matrix.
In this question, matrix 𝐴 has two rows and three columns. Therefore, its order is two by three. Matrix 𝐵 is a square two-by-two matrix with two rows and two columns. As the number of columns in matrix 𝐴 is not equal to the number of rows in matrix 𝐵, then the matrix 𝐴𝐵 is undefined.
Whilst it is not required in this question, we could calculate the matrix 𝐵𝐴 as matrix 𝐵 has two columns and matrix 𝐴 has two rows. It is important to check the order of our matrices before trying to perform matrix multiplication.
