Question

how to multiply the three matrix




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Answer 1

Let A, B, and C be matrices we are going to multiply.

According to the Associative law of matrix multiplication, we know that:

ABC = A(BC) = (AB)C

So, first we need to calculate AB or BC and the resulting matrix will be multiplied with the remaining one.

To calculate AB, the number of columns in A must equal the number of rows in B. Thus, if A is an r1∗c1 matrix(order of a matrix-rows by column) and B is an r2∗c2 matrix, c1=r2

And the product of these two matrices will have an order of r1∗c2.

Now the matrix C must have an order of r3∗c3 where c2=r3.

And the result of ABC will have an order of  r1∗c3.