AP DSC School Assistant Math Model Test 3

Concept:A square matrix where all diagonal entries are 1 and all off‑diagonal entries are 0 is called an identity matrix. We need to check whether it also belongs to the special types listed: scalar, diagonal, skew‑symmetric, symmetric.Explanation:Let the given matrix be $I = \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$.Step 1 – Diagonal matrix:Every entry where row number ≠ column number is 0. Hence $I$ is a diagonal matrix.Step 2 – Scalar matrix:A scalar matrix is a diagonal matrix where all diagonal elements are equal. Here all diagonal elements are 1 (a constant). So $I$ is a scalar matrix.Step 3 – Symmetric matrix:A matrix $A$ is symmetric if $A = A^T$. For $I$, its transpose is the same as itself, so $I$ is symmetric.Step 4 – Skew‑symmetric matrix:A matrix is skew‑symmetric if $A = -A^T$. For $I$, $I \neq -I$ (since $-I$ would have all diagonal entries –1, not 1). Hence $I$ is not skew‑symmetric.Therefore the matrix is scalar, diagonal, and symmetric, but not skew‑symmetric. Among the given choices, option A lists exactly these three types.Answer:Option A – (A), (B) and (D) only.