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Mathematics

Grade9

Easy

Question

Is the product defined of the matrices AB and BA?
$A equals open square brackets table attributes columnalign left end attributes row 1 2 end table close square brackets comma space B equals open square brackets table attributes columnalign left end attributes row 4 row 5 row 6 end table close square brackets$

AB and BA are defined.
AB and BA are not defined.
AB is not defined, and BA is defined.
AB is defined, and BA is not defined.

hint Hint:

Two matrices A and B are said to be compatible if the number of columns in A is equal to the number of rows in B. That means if A is a matrix of order m×n and B is a matrix of order n×p, then we can say that matrices A and B are compatible.

The correct answer is: AB is not defined, and BA is defined.

$A equals open square brackets table attributes columnalign left end attributes row 1 2 end table close square brackets comma space C o l u m n s space equals space 2 comma space R o w s space equals 1 space B equals open square brackets table attributes columnalign left end attributes row 4 row 5 row 6 end table close square brackets comma space R o w s space equals space 3 comma space C o l u m n s space equals space 1$
Two matrices A and B are said to be compatible
If the number of columns in A is equal to the number of rows in B. That means if A is a matrix of order m×n and B is a matrix of order n×p, then we can say that matrices A and B are compatible.
If the number of columns in A is not equal to the number of rows in B. That means if A is a matrix of order m×n and B is a matrix of order n×p, then we can say that matrices A and B are incompatible.
Thus, above matrix AB is not defined, and BA is defined.

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