dA matrix is an array of numbers arranged in rows and columns.
When asked to define the dimension of a matrix, we are asked to define it according to the number of rows (horizontal layers) and columns (vertical layers) it contains.
A matrix is defined in the form: Number of rows X Number of columns.
A)
The dimension of S is 3 x 2 because it has 3 rows and 2 columns.
B)
The dimension of P is 1 x 3 because it has 1 row and 3 columns.
C)
First we look at the rule of multiplying the matrices before we can find out the status.
Two matrices are multipliable iff the number of columns in the first is equal to the number of rows in the second.
Therefore,
SP is undefined because the number of columns in S (2) and rows in P (1) are unequal.
PS is defined because the number of columns in P (3) and rows in S (3) are equal.