If A = [aij]3×3 is a scalar matrix then which of the following must be true?

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Diagonal Matrix and Scalar Matrix, Symmetric Matrix | PadhAiPro

Question

MCQ (Single)Diagonal Matrix and Scalar MatrixSymmetric Matrix

If the sum of all the elements of a 3 × 3 scalar matrix is 9, then the product of all its elements is :

Assertion (A) : For any symmetric matrix A, B′AB is a skew-symmetric matrix. Reason (R) : A square matrix P is skew-symmetric if P′ = – P.

Transpose of a Matrix and Its Properties

Symmetric Matrix

Skew-Symmetric Matrix

Assertion (A) : Every scalar matrix is a diagonal matrix. Reason (R) : In a diagonal matrix, all the diagonal elements are 0.

If [a c 0; b d 0; 0 0 5] is a scalar matrix, then the value of a + 2b + 3c + 4d is:

The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3 × 2, then order of matrix P is :

If [2 0; 5 4] = P + Q, where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to