Q. 165.0( 2 Votes )

Show by an exampl

Answer :

We know that,

In order to multiply two matrices, A and B, the number of columns in A must equal the number of rows in B. Thus, if A is an m x n matrix and B is an r x s matrix, n = r.


We are given that,


A ≠ 0 and B ≠ 0


We need to show that, AB = 0.


For multiplication of A and B,


Number of columns of matrix A = Number of rows of matrix B = 2 (let)


Matrices A and B are square matrices of order 2 × 2.


For AB to become 0, one of the column of matrix A and other row of matrix B must be 0.


For example,




Check: Multiply AB.



Multiply 1st row of matrix A by matching members of 1st column of matrix B, then sum them up.


(0, 1).(3, 0) = (0 × 3) + (1 × 0)


(0, 1).(3, 0) = 0 + 0 = 0



Similarly, let us do it for the rest of the elements.




Thus, this example justifies the criteria.


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