This advanced calculator handles algebra, geometry, calculus, probability/statistics, linear algebra, linear programming, and discrete mathematics problems, with steps shown.
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add matrices
add vectors
adjoint (adjugate) matrix
angle between vectors
area between curves (under one curve)
area of surface of revolution
arithmetic mean
arithmetic sequence
asymptotes
average rate of change
basis
beta distribution
binomial distribution
binomial expansion
boolean algebra
box and whisker plot
center of mass (centroid) and moments
characteristic polynomial
circle properties
cofactor matrix
column space
combinations and permutations
complete the square
composite function
conic section
cosecant
cosine
cotangent
Cramer's rule
critical and saddle points, extrema (multivariable function)
critical points and extrema (single variable function)
cross product
cube root
cubic regression
curl
curvature
curve arc length
decimal to fraction
decimal to percent
definite integral (proper and improper)
degree and leading coefficient
derivative
Descartes' rule of signs
diagonalize matrix
difference quotient
direct, inverse, and joint variation
directional derivative
discriminant
distance between two points
divergence
divide matrices
divide polynomials
domain and range
dot (inner) product
eigenvalues and eigenvectors
ellipse properties
end behavior
Euler's method
evaluate function/expression
exponential distribution
exponential function
factor expression
factor polynomial
factorial
find zeros
FOIL
fraction to decimal
fraction to percent
function average value
function differential
function gradient
function intercepts
function properties
Gauss-Jordan elimination
geometric distribution
geometric mean
geometric sequence
Gram-Schmidt process
graphing
greatest common divisor (GCD)
half-life
harmonic mean
Hessian (Hesse) matrix
hyperbola properties
hyperbolic cosecant
hyperbolic cosine
hyperbolic cotangent
hyperbolic secant
hyperbolic sine
hyperbolic tangent
hypergeometric distribution
implicit derivative
improper fraction to mixed number
improved Euler (Heun's) method
indefinite integral
inflection points, concavity
instantaneous rate of change
interquartile range
inverse cosecant
inverse cosine
inverse cotangent
inverse function
inverse hyperbolic cosecant
inverse hyperbolic cosine
inverse hyperbolic cotangent
inverse hyperbolic secant
inverse hyperbolic sine
inverse hyperbolic tangent
inverse Laplace transform
inverse secant
inverse sine
inverse tangent
Jacobian
Lagrange multipliers
Laplace transform
law of cosines
law of sines
least common multiple (LCM)
left endpoint approximation for a function
left endpoint approximation for a table
limit
line equation
line slope
linear approximation
linear independence
linear regression (line of best fit)
logarithm
logarithmic differentiation (derivative)
long division of numbers
lower quartile
LU decomposition
margin of error
matrix determinant
matrix exponential
matrix inverse
matrix of minors
matrix power
matrix rank
matrix scalar multiplication
matrix trace
matrix transpose
mean value theorem
median
midpoint
midpoint rule for a function
midpoint rule for a table
mixed number to improper fraction
mode
modified Euler's method
moments of inertia and radius (radii) of gyration
Moore-Penrose inverse (pseudoinverse)
multiple (double, triple) integral
multiply matrices
multiply polynomials
normal component of acceleration
normal distribution
normal line
null space (kernel), nullity
operations on complex numbers
operations on fractions
operations on functions
operations on matrices
operations on polynomials
operations on vectors
order of operations (PEMDAS)
orthogonal complement
p-value
parabola properties
parallel/perpendicular line
partial derivative
partial fraction decomposition
Pearson correlation coefficient
percent to decimal
percent to fraction
percentile
percentile/class rank
Poisson distribution
polar form of a complex number
polar/rectangular coordinates
polar/rectangular equation
polynomial long division
polynomial roots
prime factorization
Pythagorean theorem (right triangle)
QR factorization
quadratic approximation
quadratic regression (parabola of best fit)
radius and interval of convergence
range of a data set
rational zeros theorem
reduced row echelon form (rref)
remainder theorem
Riemann sum for a function
Riemann sum for a table
right endpoint approximation for a function
right endpoint approximation for a table
roots of a complex number, unity
rotate point
row space
sample/population coefficient of variation
sample/population covariance
sample/population standard deviation
sample/population variance
scalar projection
scientific notation
secant
secant line
second derivative
series and sum
simplex method
simplify expression
Simpson's 3/8 rule for a function
Simpson's 3/8 rule for a table
Simpson's rule for a function
Simpson's rule for a table
sine
singular value decomposition
slope intercept form with two points
solve cubic equation
solve differential equation
solve equation
solve for x
solve inequality (system of inequalities)
solve quadratic equation
solve quartic equation
solve system of equations
solve system of linear equations
solve system of simultaneous equations
solve triangle
square root
subtract matrices
subtract vectors
synthetic division
tangent
tangent line
tangent plane
tangential component of acceleration
Taylor (Maclauring) series
torsion
transition matrix
trapezoidal rule for a function
trapezoidal rule for a table
trigonometry
triple product
truth table
unit binormal vector
unit normal vector
unit tangent vector
unit vector
upper quartile
vector magnitude
vector projection
vector scalar multiplication
volume of solid of revolution
Wronskian
z-score
3d graphing
4th (fourth) order Runge-Kutta method
5 (five) number summary
Solution The classical adjoint, adjugate, or adjunct of a square matrix is the transpose of its cofactor matrix.
The cofactor matrix is $$$ \left[\begin{array}{cc}d & - c\\- b & a\end{array}\right]$$$ (for steps, see cofactor matrix calculator ).
The transpose of the cofactor matrix is $$$ \left[\begin{array}{cc}d & - b\\- c & a\end{array}\right]$$$ (for steps, see matrix transpose calculator ).
Answer The adjoint matrix is $$$ \left[\begin{array}{cc}d & - b\\- c & a\end{array}\right]$$$ A .
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