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

If A = `[(0, -x),(x, 0)]`, B = `[(0, 1),(1, 0)]` and x² = –1, then show that (A + B)² = A² + B². 

If A = `[(1, 2),(4, 1)]`, find A² + 2A + 7I.

Matrix multiplication is ______ over addition.

Matrices of any order can be added.

`"A" = [(1,-1),(2,-1)], "B" = [("x", 1),("y", -1)]` and (A + B)² = A² + B², then x + y = ____________.

If `[(2"a"+"b", "a"-2"b"),(5"c" - "d", 4"c"+3"d")] = [(4, -3),(11, 24)]`, then value of a + b – c + 2d is:

If A `= [(0,2),(2,0)],` then A² is ____________.

`[(1,1,2),(1,3,1),(3,2,1)]`

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b

If A= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.

If A is a skew symmetric matric of order 3, then prove that det A  = 0

If `A = [(-1,2,3),(5,7,9),(-2,1,1)]  "and"  B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A+ B)' = A' + B'

if `A = [(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A- B)' = A' - B'

if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A + B)' = A' + B'

if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A - B)' = A' - B'

if A' = `[(-2,3),(1,2)] and B = [(-1,0),(1,2)]`  then find (A + 2B)'

For the matrices A and B, verify that (AB)′ = B'A' where `A =[(1),(-4), (3)], B = [-1, 2  1]`

For the matrices A and B, verify that (AB)′ = B'A'  where `A =[(0), (1),(2)] , B =[1 , 5, 7]`

If A = `[(cos alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that  A' A = I

If A = `[(sin alpha, cos alpha), (-cos alpha, sin alpha)]` then verify that  A'A = I