Let A be a matrix of order \(3 \times 2\). If \(I_m\) and \(I_n\) are identity matrices such that \(I_m A = A\) and \(A I_n = A\), then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(m = 3,\ n = 2\)
A product PQ is defined only when the number of columns of P equals the number of rows of Q.
In \(I_m A\), the identity matrix \(I_m\) has m columns and A has 3 rows, so
\(m = 3\)
In \(A I_n\), A has 2 columns and \(I_n\) has n rows, so
\(n = 2\)
Both products are then of order \(3 \times 2\), the same as A.