Answer:
Dimensions of the product matrix = (3 × 3)
Explanation:
If matrix P having dimensions (m × n) and matrix Q having dimensions (n × r) are multiplied,
Dimensions of the product matrix PQ will have the dimensions as (m × r).
That means product of the two matrices are defined when columns of first matrix P is equal to the rows of the second matrix Q.
Following this rule,
Dimensions of matrix A = (2 × 3)
[ Rows × Columns]
Dimensions of matrix B = (3 × 3) [Rows of B = 3, columns of B = 3]
Dimensions of matrix C = (3 × 2) [Rows of C = 3, columns of C = 2]
Since columns of C and rows of A are equal.
Therefore, product of C and A is defined.
Product of the matrices C & A will have the dimensions as (3 × 3).