Q. 415.0( 2 Votes )

If A is a matrix

Answer :

We are given that,

Order of matrix A = 3 × 4


Order of matrix B = 4 × 3


We need to find the order of the matrix of AB.


We know that,


For matrices X and Y such that,


Order of X = m × n


Order of Y = r × s


In order to multiply the two matrices X and Y, the number of columns in X must be equal to the number of rows in Y. That is,


n = r


And order of the resulting matrix, XY is given as


Order of XY = m × s


Provided n = r.


So, we know


Order of A = 3 × 4


Here,


Number of rows = 3


Number of columns = 4


Order of B = 4 × 3


Here,


Number of rows = 4


Number of columns = 3


Note that,


Number of columns in A = Number of rows in B = 4


So,


Order of the resulting matrix, AB is given as


Order of AB = 3 × 3


Thus, order of AB = 3 × 3


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