Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

If A is a square matrix, then AA is a

If A and B are symmetric matrices, then ABA is

If A = [a_ij] is a square matrix of even order such that a_ij = i² − j², then 

If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\]  is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is  

If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is 

If A and B are matrices of the same order, then AB^T − BA^T is a 

The matrix  \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a 

The matrix   \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is

Show that a matrix which is both symmetric and skew symmetric is a zero matrix.

Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`

Let A = `[(2, 3),(-1, 2)]`. Then show that A² – 4A + 7I = O. Using this result calculate A⁵ also.

If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.

If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.

If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A² – B² 

Show that A′A and AA′ are both symmetric matrices for any matrix A.

If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A^–1 = A′, find value of α

If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.

If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.

Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.

The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.