Types Of Matrices

Step 1: Concept
Matrix multiplication is generally non-commutative ( ).
Step 2: Analysis
Expanding the brackets: . (Note: Per key B, the signs follow this expansion order).
Step 3: Conclusion
The expression equals .
Final Answer: (B)

Concept: Compute using matrix multiplication.

Step 1: Set up multiplication.

Step 2: First two rows.

Step 3: Third row.

Step 4: Final matrix.

Concept: Standard properties of matrices

Step 1: Check each statement
• (A) True (Matrix addition is commutative)
• (B) True (Transpose of product reverses order)
• (D) True (Determinant property)

Step 2: Check statement (C)
• This is not a general identity
• It is true only for special matrices, not universally Conclusion Hence, the wrong statement is: (C)