Statement 1: If A and B are two matrices such that AB = A, then B is a square matrix
and
Statement 2: The product AB exists only if A is of order m × n and B is of order n × n.
1.
Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1.
2.
Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statement 1.
3.
Statement 1 is True, statement 2 is False.
4.
Statement 1 is False, statement 2 is True.
-1 out of 3 marks
Correct Answer: 1
Solution:
Ans: (1)
1not necessarily... only required condition is dat "no. of rows in second matrix must b equal to no. of coloumns in first matrix... to multiply two matrices..."
well, u can also conclude lyk dis... AB=A => B is an identity matrix, and identity matrices are always square matrices... :)
1so in stmt 2 : there can b any value in n x __ ....And it will bcome stmt 2 as wrong one....
1nope... see let me tell u clearly now...
dis is d basic step of multiplication...
(m x n).(n x p) = (m x p) ...... rite...!!!
now since RHS is A... and first matrix in LHS is also A, so both of them should have same order... i.e., (m x n)... hence p=n... which implies dat order of B must be (n x n)... implies it has to b a square matrix...
got it now... :)
11The second statement is wrong i too answered it the same way
@mak
it is not true because for only the product to be defined the order of B can be nxp (p ≥1)
1oh yeah... i'm sorry... i read statement 2 in ref. wid statement 1... so made dat blunder...
well, considering statement 2 individually, it's false... i agree... :)
