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.

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Transpose of a Matrix and Its Properties, Symmetric Matrix, Skew-Symmetric Matrix | PadhAiPro

Question

Assertion-ReasonTranspose of a Matrix and Its PropertiesSymmetric MatrixSkew-Symmetric MatrixCBSE PYQ

If A and B are two skew symmetric matrices, then (AB + BA) is :

If A is a square matrix of order 3 such that the value of |adj·A| = 8, then the value of |Aᵀ| is :

Determinant of a Square Matrix

Adjoint of a Square Matrix

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

A and B are skew-symmetric matrices of same order. AB is symmetric, if :

For what value of x ∈ [0, π/2], is A + A′ = √3 I, where A = [cos x sin x; −sin x cos x] ?

If a matrix A = [1 2 3], then the matrix AA' (where A' is the transpose of A) is :