Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

If A and B are symmetric matrices, then AB – BA is a ______.

If A and B are symmetric matrices, then BA – 2AB is a ______.

If A is symmetric matrix, then B′AB is ______.

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

If A and B are any two matrices of the same order, then (AB)′ = A′B′.

AA′ is always a symmetric matrix for any matrix A.

If A is skew-symmetric matrix, then A² is a symmetric matrix.

If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.

If A and B are symmetric matrices of the same order, then ____________.

If A and B are symmetric matrices of the same order, then ____________.

If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.

If A is any square matrix, then which of the following is skew-symmetric?

If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.

The diagonal elements of a skew symmetric matrix are ____________.

If A = [a_ij] is a skew-symmetric matrix of order n, then ______.

If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.

Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.

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