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Class 12MathematicsMatrixIntroduction to matricesEasy
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Let \(A=\begin{bmatrix}5&0\\0&5\end{bmatrix}\). What type of matrix is \(A\)?

Answer and explanation

Correct answer: Scalar matrix

\(A\) has the form \(\begin{bmatrix}5&0\\0&5\end{bmatrix}=5\begin{bmatrix}1&0\\0&1\end{bmatrix}=5I\). When a diagonal matrix has the same non-zero value on all diagonal entries (so it equals a constant times the identity matrix), it is a scalar matrix. Hence \(A\) is a scalar matrix.

Related tags

MatrixTypes Of MatricesScalar MatrixIdentity
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10 more MCQs
  1. 1If a matrix has (3) rows and (4) columns, how many elements does it have?
  2. 2In the matrix \(A=[a_{ij}]_{2\times3}\), what does \(i\) represent?
  3. 3What does (a_{23}) mean in the matrix (A=[a_{ij}])?
  4. 4What type of matrix is (A=\begin{bmatrix}1&0\\0&1\end{bmatrix})?
  5. 5Which matrix is a square matrix?
  6. 6What is the value of \(a_{12}\) in \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\)?
  7. 7What is the value of \(a_{21}\) in the matrix \(A=\begin{bmatrix}6&7&8\\9&10&11\end{bmatrix}\)?
  8. 8When are two matrices (A) and (B) called equal?
  9. 9If \(A=[a_{ij}]_{2\times2}\) and \(a_{ij}=i+j\), what is the value of \(a_{22}\)?
  10. 10If \(A=[a_{ij}]\) is a \(3\times2\) matrix and \(a_{ij}=2i-j\), what is the value of \(a_{31}\)?
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