Consider the matrix multiplication M A times B where A 4 3

Consider the matrix multiplication M = A times B, where A= (-4 3 6 3 -9 -2 -4 -5) and B = (-7 -1 4 -6 -6 5 0 8 0 -6 -3 -2 -6 5 -9) Is the multiplication A times B legitimate? The dimensions of the product matrix are is the multiplication B times A legitimate?

Solution

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Dimensions of matrix A = 4 X 2

Dimensions of matrix B = 3 X 5

Now for legitimate multiplication, number of columns of matrix 1 should be equal to number of rows of Matrix 2

For A X B = matrix multiplication is not legitimate

For B X A = also matrix multiplication not legitimate