With reference to square matrices, which one of the following statements is NOT correct ?
Answer & explanation
Correct answer: option 4
$\text{Check each statement:}$
$(1)\;A^T=A \Rightarrow A \text{ is symmetric}$ — $\text{True}.$
$(2)\;A^T=-A \Rightarrow A \text{ is skew-symmetric}$ — $\text{True}.$
$(3)\;\text{Multiplication of two square matrices of same order is not necessarily commutative}$ — $\text{True}.$
$(4)\;\text{The inverse of a square matrix (if it exists) is not unique}$ — $\text{False (inverse is unique).}$
$\text{NOT correct statement: Option 4.}$