If A, B, C and D are matrices of order \( 2\times n \), \( 3\times k \), \( 2\times p \) and \( n\times 3 \) respectively and AB + CD defined, then order of DB is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3\times 3 \)
The product \( AB \) is defined only when the columns of \( A \) equal the rows of \( B \), so \( n=3 \).
Then \( CD \) has order \( 2\times 3 \), because \( C \) is \( 2\times p \) and \( D \) is \( n\times 3 \).
The sum \( AB+CD \) needs both matrices to have the same order. Since \( AB \) has order \( 2\times k \), we get \( k=3 \).
So \( B \) is \( 3\times 3 \) and \( D \) is also \( 3\times 3 \), and the product \( DB \) has order \( 3\times 3 \).