Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

If A = `[(1, 0, -1),(2, 1, 3 ),(0, 1, 1)]`, then verify that A² + A = A(A + I), where I is 3 × 3 unit matrix.

If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (2A + B)′ = 2A′ + B′

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A + (B + C) = (A + B) + C

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (a + b)B = aB + bB

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)'