How do you find the inverse of #A=((2, -1, 0, 0), (-1, 2, 0, 0), (0, 0, 2, -1), (0, 0, -1, 2))#? Precalculus Matrix Algebra Inverse Matrix 1 Answer Cesareo R. Aug 27, 2016 #A^(-1) =1/3( (2, 1, 0, 0), (1, 2, 0, 0), (0, 0, 2, 1), (0, 0, 1, 2) )# Explanation: #A=((2, -1, 0, 0), (-1, 2, 0, 0), (0, 0, 2, -1), (0, 0, -1, 2))# is composed of two submatrices #A = ((a,0_2),(0_2,a))# with #a=((2,-1),(-1,2))# and #0_2=((0,0),(0,0))# so #A^(-1) = ((a^(-1),0_2),(0_2,a^(-1)))# and #a^(-1) = 1/3((2,1),(1,2)) # so #A^(-1) =1/3( (2, 1, 0, 0), (1, 2, 0, 0), (0, 0, 2, 1), (0, 0, 1, 2) )# Answer link Related questions What is the multiplicative inverse of a matrix? How do I use an inverse matrix to solve a system of equations? How do I find an inverse matrix on a TI-84 Plus? How do I find the inverse of a #2xx2# matrix? How do I find the inverse of a #3xx3# matrix? How do I find an inverse matrix on an Nspire? What is the meaning of the phrase invertible matrix? The given matrix is invertible ? first row ( -1 0 0 ) second row ( 0 2 0 ) third row ( 0 0 1/3 ) How do you find the inverse of #A=##((2, 4, 1),(-1, 1, -1), (1, 4, 0))#? How do you find the inverse of #A=##((1, 1, 1, 0), (1, 1, 0, -1), (0, 1, 0, 1), (0, 1, 1, 0))#? See all questions in Inverse Matrix Impact of this question 1726 views around the world You can reuse this answer Creative Commons License